VASPKIT—VASP软件预-后处理工具介绍

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VASPKIT---VASP软件预-后处理工具介绍

VASPKIT---VASP软件预-后处理工具介绍 1. VASPKIT简介 2. VASPKIT的配置和使用 3. VASPKIT的子功能介绍 3.1 VASP输入文件的生成和检查 3.2 能带计算 PBE泛函计算能带 HSE06杂化泛函计算能带 3.3 分波态密度和局域态密度 3.4 热力学量校正气相分子的热力学校正吸附质分子的热力学校正 3.5 差分电荷密度图的绘制 3.6. 催化相关将NEB路径转成PDB文件以可视化线性插点生成NEB的路径虚频校正估算一级反应的反应速率和半衰期结构操作小工具 3.7. 能带反折叠计算 3.8 3D能带计算 3.9 费米面计算 3.10 VASP2BoltzTraP接口 3.11 基于能量-应变关系计算弹性常数 3.12 用VASPKIT计算有效质量 3.13 绘制原子电荷着色的结构图 4. 用户自定义界面（测试功能）二维材料MoS2投影能带计算(不考虑自旋极化和旋轨耦合) 5. VASPKIT命令行批量操作 6. VASPKIT的引用和手册开发不易，你的打赏是对开发者的鼓励。 Appendix：菜单功能介绍
1. VASPKIT简介

VASP 的全称 Vienna Ab-initio Simulation Package ，是维也纳大学Hafner小组开发的进行电子结构计算和量子力学-分子动力学模拟软件包。它是目前材料模拟和计算物质科学研究中最流行的商用软件之一。与Material Studio软件包中的 CASTEP 功能类似，但是 VASP 的精度相对要高一点。不同于 CASTEP 的图形界面， VASP 是一套没有界面的计算软件，建模、可视化、数据分析都需要依赖第三方工具如P4VASP、ASE、Pymatgen、VESTA软件等。VESTA、P4VASP主要是用来建模、可视化和分析部分数据。而ASE、Pymatgen这些软件擅长于数据处理，但是安装比较麻烦，同时入门门槛比较高，需要使用者有一定的编程水平。 VASP 用户的学科分布很广，有做催化的，有做光学的，有做材料的，各个领域的数据后处理方式大相径庭。很多用户开发并贡献了自己所在领域用到的的脚本或者小程序，本人就开发了一款用来处理结构文件的 POSCARtookit 脚本。但是对于新用户来说，找到并成功使用这些脚本是不太容易的。因此一款容易上手、功能强大的预-后数据处理软件 vaspkit 应运而生。最新版的 vaspkit 是王伟老师、许楠、刘锦程，唐刚，李强和乐平共同努力的成果。 vaspkit 0.72 版本相对于之前的版本做了很多菜单调整，将功能相似的进行了归类，优化了一些已有功能，并增加了一些与催化有关的功能。 VASPKIT release 版本是一款用 FORTRAN 编写，在 LINUX 环境下运行的二进制软件。它几乎不依赖于其他库，软件体积仅仅5.0M，无需安装即可使用，同时 EXAMPLES 目录下面有主要功能的测试例子，方便用户学习使用。
主要功能有 ：1.自动生成VASP计算所需的必备文件，包括INCAR、POTCAR、POSCAR等，并对其进行格式检查 2.结构对称性查找 3.催化方面的工具，根据层数或者高度区间固定原子，NEB路径生成、NEB路径生成可视化的PDB文件、虚频校正等。 4.生成晶体的能带路径（包括杂化泛函），并处理能带数据 5.处理态密度DOS和投影态密度PDOS 6.处理电荷密度、静电势，绘制是空间波函数 7.其他功能，比如热力学量校正（吸附质分子和气相分子），光学、分子动力学、导电率和半导体方面的小工具。

详细可见附录：VASPKIT菜单功能介绍
0.73版本新增功能和修复的BUGs
Added support to determine independent elastic stiffness tensor by polynomial fitting of the energies vs strain relationships for bulk materials (task 201, except triclinic crystal system).
Added support to read elastic stiffness tensor from OUTCAR file and calculate various mechanical properties for polycrystalline bulk materials (task 203).
Added support to find conventional cell (task 603);
Added support to redefine lattice (task 400);
Added support to swap the axis of lattice vector (task 407);
Added support to Bader2PQR module contributed by J.C.LIU@THU (task 508);
Added support to convert cif files with no fractional occupations to POSCAR (task 105);
Added support to generate BAND_GAP file when extracted band structure data (tasks 211 and 252);
Added support to print out the average d band center in both spin up and spin down channels within the specified energy interval for each atom (task 503);
Added the parameter PLOT_MATPLOTLIB in ~/.vaspkit file to control whether the band-structure and DOS plots will be written; For more details see vaspkit/how_to_set_environment_variable file for reference;
Added the parameter USER_DEFINED_INCAR in ~/.vaspkit file to control whether to use embedded INCAR templates or user defined INCAR templates, need to set VASPKIT_UTILITIES_PATH variable first; For more details see vaspkit/how_to_set_environment_variable file for reference;
Added support to generate SELECTED_ATOM_LIST file when sum over PDOS (task 114) and PBAND (tasks 214 and 255) for selected atoms;
Fixed a bug in extracting projected density-of-states in non-collinear calculations pointed by G.Tang@BIU and other users;
Fixed a bug in generating K-Path for rectangular 2D-Bravais lattice pointed by X.U.LIU@GZU;
Fixed a bug in generating the KPOINTS file for band-unfolding calculations pointed by T.J.SHAO@WIPM;
Fixed a bug in evaluating the band gap values for spin-polarized systems when set the parameter SET_FERMI_ENERGY_ZERO to .TRUE. in the ~/.vaspkit file;
Minor bug fixes and significant optimizations.
2. VASPKIT的配置和使用

vaspkit 是一款运行在LINUX环境下的软件，为了确保能够使用 vaspkit 的完整功能。用户可以配置 vaspkit 的环境目录，在下一次运行时生效。通过在 bash 终端下运行以下命令将环境变量文件复制到用户目录下。
<a class="md-header-anchor" name="header-n46"></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"/><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-builtin">cp</span> <span class="cm-attribute">-f</span> how_to_set_environment_variable ~/.vaspkit</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>并编辑<code>.vaspkit</code>文件</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-builtin">vi</span> ~/.vaspkit</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>该配置文件主要用来设置<code>vaspkit</code>的环境变量,包括VASP版本信息，赝势库的目录，泛函方法的选择，并选择是否按照VASP官方的推荐生成元素的赝势文件，设置生成的INCAR模板是覆盖、追加还是备份原有的INCAR。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>11</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"># cp how_to_set_environment_variable ~/.vaspkit and modify the ~/.vaspkit file based on your settings!    </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">VASP5                    .TRUE.             # .TRUE. or .FALSE.; Set .FALSE. if using vasp.4.x </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">GGA_PATH                 '~/POTCAR/GGA'     #  Path of GGA potential. </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">PBE_PATH                 '~/POTCAR/PBE'     #  Path of PBE potential. </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">LDA_PATH                 '~/POTCAR/LDA'     #  Path of LDA potential. </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">POTCAR_TYPE               PBE               #  PBE, GGA or LDA; </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">GW_POTCAR                .FALSE.            # .TRUE. or .FALSE.;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">RECOMMENDED_POTCAR       .TRUE.             # .TRUE. or .FALSE.; </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">MINI_INCAR               .FALSE.            # .TRUE. or .FALSE.; </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">SET_FERMI_ENERGY_ZERO    .TRUE.             # .TRUE. or .FALSE.;  </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">SET_INCAR_WRITE_MODE     OVERRIDE           #  OVERRIDE, APPEND,BACK-UP-OLD,BACK-UP-NEW; </span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 280px;"/><div class="CodeMirror-gutters" style="height: 280px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>设置好POTCAR的目录和完成一些其他的设置后，就可以启动<code>vaspkit</code>了。
为了方便，可以将<code>vaspkit</code>的绝对路径加入到环境变量里，如果是LINUX的用户，可以这样操作：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>2</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-builtin">echo</span> <span class="cm-string">'export PATH=/home/vaspkit.0.73/bin/:$PATH'</span> >> ~/.bashrc</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-builtin">source</span> ~/.bashrc</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 40px;"/><div class="CodeMirror-gutters" style="height: 40px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>其中<code>/home/vaspkit.0.73/bin/</code>用自己的<code>vaspkit</code>可执行文件所在<code>bin</code>目录的绝对路径替代。</p><blockquote><p><code>vaspkit</code>自<code>0.73</code>版之后<strong>提供了自动配置脚本</strong><code>setup.sh</code>，<code>source setup.sh</code> 或者<code>bash setup.sh</code>可以完成配置。对于新用户来说非常友好，但是赝势目录还需自己设置。如果已经存在<code>~/.vaspkit</code>，将不会覆盖它，仍使用老版本的环境变量。</p></blockquote><p>在终端直接输入<code>vaspkit</code>或者<code>/home/vaspkit.0.73/bin/vaspkit</code>开始运行<code>vaspkit</code>程序。不出意外，你将会得到一个与我展示的一致的，非常萌的界面：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><span><span></span>x</span></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">            \\\///</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">           / _  _ \       Hey, you must know what you are doing.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">         (| (.)(.) |)     Otherwise you might get wrong results!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +-----.OOOo--()--oOOO.------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |       A Pre- and Post-Processing Program for VASP Code        |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |           VASPKIT Version: 0.73 (18 Apr. 2019)                |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |            Developed by Vei WANG (wangvei@me.com)             |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |            Contributor: Nan XU (tamas@zju.edu.cn)             |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +-----.oooO-----------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">        (   )   Oooo.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">         \ (    (   )</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">          \_)    ) /</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                (_/</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ===================== Structural Options ========================</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 1)  VASP Input Files Generator    2)  Elastic-Properties</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 3)  K-Path Generator              4)  Structure Editor</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 5)  Catalysis-ElectroChemi Kit    6)  Symmetry Search</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">18</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">19</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ===================== Electronic Options ========================</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">20</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 11) Density-of-States             21) DFT Band-Structure</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">21</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 23) 3D Band-Structure             25) Hybrid-DFT Band-Structure</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">22</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 26) Fermi-Surface                 28) Band-Structure Unfolding</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">23</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">24</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> =========== Charge & Potential & Wavefunction Options ===========</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">25</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 31) Charge & Spin Density         42) Potential-Related</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">26</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 51) Wave-Function Analysis</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">27</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ====================== Misc Utilities ===========================</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">28</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 71) Linear Optics                 72) Molecular-Dynamics Kit</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">29</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 73) VASP2BoltzTraP Interface</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">30</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 91) Semiconductor Calculator      92) 2D-Materials Kit</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">31</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">32</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 0)  Quit</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">33</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ------------>></span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 660px;"/><div class="CodeMirror-gutters" style="height: 660px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>如果出现以下问题,说明你的LINUX运行依赖库版本太低，需要升级（不建议），可以联系开发者获得在低版本LINUX环境下编译的版本。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">vaspkit: /lib64/libc.so.6: version <span class="cm-quote">`GLIBC_2.14' not found (required by vaspkit)</span></span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>如果出现<code>-bash: line 7: ./vaspkit: Permission denied</code>权限问题，只需赋予<code>vaspkit</code>执行权限即可：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-builtin">chmod</span> u<span class="cm-operator">+</span>x /home/vaspkit.0.73/bin/vaspkit</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><h3><a name="header-n65" class="md-header-anchor "/>3. VASPKIT的子功能介绍</h3><p>本教程将介绍使用<code>vaspkit</code>生成VASP的输入文件，使用PBE和HSE06计算能带，提取分析分波态密度和局域态密度，校正热力学量计算自由能、生成差分电荷密度, 催化相关的工具和能带反折叠计算。能带计算包含了使用普通泛函和杂化泛函两个例子，而热力学量校正主要计算零点振动能及温度对自由能和焓的贡献。</p><h4><a name="header-n67" class="md-header-anchor "/>3.1 VASP输入文件的生成和检查</h4><p>为了成功运行VASP计算任务，我们至少需要4个文件：INCAR、POSCAR、POTCAR及KPOINTS，INCAR是告诉 VASP算什么任务，怎么算的控制文件；POSCAR是包含晶格信息，原子坐标信息和原子速度信息（MD用）的文件；POTCAR是赝势文件，也就是将内层电子用势函数表示；KPOINTS（可包含在INCAR内，不推荐省略）包含了倒易空间内K点信息，波函数会在这些点上积分得到电荷密度。
<code>vaspkit 0.71</code>以后的版本将K点生成、POTCAR生成和INCAR生成整合到了功能<code>1</code>：<code>VASP Input Files Generator</code>中。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>9</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 101) Customize INCAR File</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 102) Generate KPOINTS File for SCF Calculation</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 103) Generate POTCAR File with Default Setting</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 104) Generate POTCAR File with User Specified Potential</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 105) Generate POSCAR File from cif (no fractional occupations)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 106) Generate POSCAR File from Material Studio xsd (retain fixes)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 107) Reformat POSCAR File in Specified Order of Elements</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 108) Successive Procedure to Generate VASP Files and Check</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 109) Check All VASP Files</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 180px;"/><div class="CodeMirror-gutters" style="height: 180px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>下面展示怎么使用<code>vaspkit</code>进行一个VASP计算任务。
<code>POSCAR</code>一般由软件生成或者从数据库中获得，简单体系可自己搭建。本例中从数据库（<a href="http://www.catalysthub.net/" target="_blank" class="url">http://www.catalysthub.net/</a>）中获得<strong>纤锌矿ZnO</strong>的POSCAR文件（也可以下载CIF文件，然后通过<code>vaspkit</code>的功能<code>105</code>或者<code>VESTA</code>转化成POSCAR文件，只是原子位置分数占据的问题需要注意）。在<code>catalysthub</code>中检索<code>ZnO</code>，检索结果如下所示。纤锌矿ZnO的为六方晶系，空间群为<code>P63mc</code>。因此下载第二行的POSCAR，下载的文件名为<code>ZnO-1811117.vasp</code>。置于<code>vaspkit.0.73/examples/ZnO_optimization</code>目录下。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>8</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">The following shows the results (4) for: ZnO</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" class="cm-tab-wrap-hack" style="padding-right: 0.1px;">Full formula<span class="cm-tab" role="presentation" cm-text="	">    </span>Space group<span class="cm-tab" role="presentation" cm-text="	"> </span>HM<span class="cm-tab" role="presentation" cm-text="	">  </span>HALL<span class="cm-tab" role="presentation" cm-text="	">    </span>Lattice system<span class="cm-tab" role="presentation" cm-text="	">  </span>Band gap<span class="cm-tab" role="presentation" cm-text="	">    </span>Structure file<span class="cm-tab" role="presentation" cm-text="	">  </span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" class="cm-tab-wrap-hack" style="padding-right: 0.1px;">Zn1O1<span class="cm-tab" role="presentation" cm-text="	">   </span>216<span class="cm-tab" role="presentation" cm-text="	"> </span>F-43m<span class="cm-tab" role="presentation" cm-text="	">   </span>F -4 2 3<span class="cm-tab" role="presentation" cm-text="	">    </span>Cubic<span class="cm-tab" role="presentation" cm-text="	">   </span>0.63110 eV<span class="cm-tab" role="presentation" cm-text="	">  </span>CIF | POSCAR | LAMMPS<span class="cm-tab" role="presentation" cm-text="	">   </span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" class="cm-tab-wrap-hack" style="padding-right: 0.1px;">Zn2O2<span class="cm-tab" role="presentation" cm-text="	">   </span>186<span class="cm-tab" role="presentation" cm-text="	"> </span>P63mc<span class="cm-tab" role="presentation" cm-text="	">   </span>P 6c -2c<span class="cm-tab" role="presentation" cm-text="	">    </span>Hexagonal<span class="cm-tab" role="presentation" cm-text="	">   </span>0.73170 eV<span class="cm-tab" role="presentation" cm-text="	">  </span>CIF | POSCAR | LAMMPS<span class="cm-tab" role="presentation" cm-text="	">   </span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" class="cm-tab-wrap-hack" style="padding-right: 0.1px;">Zn1O1<span class="cm-tab" role="presentation" cm-text="	">   </span>225<span class="cm-tab" role="presentation" cm-text="	"> </span>Fm-3m<span class="cm-tab" role="presentation" cm-text="	">   </span>-F 4 2 3<span class="cm-tab" role="presentation" cm-text="	">    </span>Cubic<span class="cm-tab" role="presentation" cm-text="	">   </span>0.71940 eV<span class="cm-tab" role="presentation" cm-text="	">  </span>CIF | POSCAR | LAMMPS<span class="cm-tab" role="presentation" cm-text="	">   </span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" class="cm-tab-wrap-hack" style="padding-right: 0.1px;">Zn1O1<span class="cm-tab" role="presentation" cm-text="	">   </span>221<span class="cm-tab" role="presentation" cm-text="	"> </span>Pm-3m<span class="cm-tab" role="presentation" cm-text="	">   </span>-P 4 2 3<span class="cm-tab" role="presentation" cm-text="	">    </span>Cubic<span class="cm-tab" role="presentation" cm-text="	">   </span>0.00000 eV<span class="cm-tab" role="presentation" cm-text="	">  </span>CIF | POSCAR | LAMMPS<span class="cm-tab" role="presentation" cm-text="	">   </span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 180px;"/><div class="CodeMirror-gutters" style="height: 180px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>接下来进行晶格优化得到合理的结构。将其改名为POSCAR文件。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-builtin">cp</span> <span class="cm-attribute">-f</span> ZnO-1811117.vasp POSCAR</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><blockquote><p>Material Studio是常用的构建模型和可视化结构的软件，MS中的结构亦可借助其它工具转换成<code>POSCAR</code>。目前常用的做法是在MS中导出<code>cif</code>文件，再通过功能<code>105</code>或者<code>vesta</code>转换成<code>POSCAR</code>。但是转换颇为麻烦并且会丢失原子的位置限制信息。因此赵焱老师开发了固定原子坐标perl小脚本<a href="https://mp.weixin.qq.com/s/F82Hzh4saiOpp4xLFU_HGg">xsd2pos.pl</a>，可以在MS中运行<code>perl</code>脚本将结构生成<code>POSCAR</code>,链接里有详细的操作流程，这里不再赘述。<code>vaspkit</code>开发者也开发了一款类似的后处理脚本，能够将含有位置固定信息的<code>xsd</code>批量转换成·<code>POSCAR</code>，并将此脚本集成到了<code>vaspkit</code>的<code>106</code>功能中。<code>xsd</code>中可以包含<code>Fix Fractional Position</code>或者<code>Fix Cartesian Position</code>两种限制方式。</p></blockquote><p>我们采用<code>vaspkit</code>预设的INCAR<code>组合</code>生成所需的INCAR文件。在有POSCAR的目录下运行<code>vaspkit</code>,输入<code>1</code>选择功能<code>VASP Input Files Generator</code>，然后输入<code>101</code>选择<code>Customize INCAR File</code>，会得到以下的显示信息：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>22</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +-------------------------- Warm Tips --------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                You MUST Know What You Are Doing</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  Some Parameters in INCAR File Neet To Be Set/Adjusted Manually</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ======================== INCAR Options ==========================</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ST) Static-Calculation            SR) Standard Relaxation</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> MG) Magnetic Properties           SO) Spin-Orbit Coupling</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> D3) DFT-D3 no-damping Correction  H6) HSE06 Calculation</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> PU) DFT+U Calculation             MD) Molecular Dynamics</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> GW) GW0 Calculation               BS) BSE Calculation</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> DC) Elastic Constant              EL) ELF Calculation</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> BD) Bader Charge Analysis         OP) Optical Properties</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> EC) Static Dielectric Constant    PC) Decomposed Charge Density</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> FD) Phonon-Finite-Displacement    DT) Phonon-DFPT</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> NE) Nudged Elastic Band (NEB)     DM) The Dimer Method</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> FQ) Frequence Calculations        LR) Lattice Relaxation</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">18</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 0)   Quit</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">19</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 9)   Back</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">20</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ------------>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">21</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Input Key-Parameters (STH6D2 means HSE06-D2 Static-Calcualtion)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">22</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> LR</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 440px;"/><div class="CodeMirror-gutters" style="height: 440px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>输入<code>LR</code>，就会得到一个预设好的用于做晶格弛豫任务的INCAR（<strong><em>有些模板需要手动修改。比如DFT+U的U值设定，NEB的IMAGES数目等</em></strong>）。如果已经有INCAR文件，则原来的INCAR文件会被覆盖。你可以编辑<code>~/.vaspkit</code>更改INCAR的输出设置。只需将最后一行的<code>SET_INCAR_WRITE_MODE</code>由默认的<code>OVERRIDE</code>更改为 <code>APPEND,BACK-UP-OLD,BACK-UP-NEW</code>中的一个，分别对应于新的内容增加到原有的INCAR后面，备份原有的INCAR再写入新的INCAR和写入到新的INCAR.new里面。
接下来生成KPOINTS文件。对于非能带计算，只需用程序自动撒点的方式，但是需要用户选择撒点方式和K点密度。具体内容可以参考李强的教程<code>Learn VASP The Hard Way （Ex1）: VASP基本输入文件的准备</code>。启动<code>vaspkit</code>,输入<code>1</code>选择功能<code>VASP Input Files Generator</code>，然后输入<code>102</code>选择功能<code>Generate KPOINTS File for SCF Calculation</code>，接下来输入<code>2</code>选择<code>Gamma Scheme</code>撒点方式（稳妥的选择），会得到以下的显示信息：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>10</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">-->> (1) Reading Lattices & Atomic-Positions from POSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +-------------------------- Warm Tips --------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   * Accuracy Levels: (1) Low: 0.06~0.04;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                      (2) Medium: 0.04~0.03;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                      (3) Fine: 0.02-0.01.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                      (4) Gamma-Only: 0.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   * 0.04 is Generally Precise Enough!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Input KP-Resolved Value (unit: 2*PI/Angstrom):</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ------------>></span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 200px;"/><div class="CodeMirror-gutters" style="height: 200px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>根据提示<code>0.04</code>已经足够精确了，因此输入<code>0.04</code>，将会得在当前目录下得到KPOINTS和POTCAR(自动生成)文件。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>2</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (2) Written KPOINTS File!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (3) Written POTCAR File with the Recommended Potential!</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 40px;"/><div class="CodeMirror-gutters" style="height: 40px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>KPOINTS内容如下：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>5</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">K-Mesh Generated with KP-Resolved Value : 0.040</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">0</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Gamma</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   9   9   5</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">0.0  0.0  0.0</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 100px;"/><div class="CodeMirror-gutters" style="height: 100px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p><code>Learn VASP The Hard Way Ex19 谁偷走的我的机时？（三）</code>提到了一个简单的K点数目判断准则，对于半导体k点数目乘实空间对应晶矢量大于20Å（参考下图），本例中ka=29.62Å已经符合经验规律。刘锦程提到对于非正交体系 ，倒格矢长度和晶常数不满足反比关系，所以采用ka≈kb≈kc的经验准则并不能保证 K点密度在各个方向长相等。而<code>vaspkit</code>严格计算了倒空间晶格矢量比例，<strong>选用经验“步长”（倒空间长度除以K点数目）0.03~0.04</strong>，<code>vaspkit</code>就能根据所选的K点密度自动生成各个方向的K点数，此时倒空间K点的<strong>resolution</strong> 为<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.214ex" height="3.002ex" viewbox="0 -983.8 5258.8 1292.6" role="img" focusable="false" style="vertical-align: -0.717ex;"><defs><path stroke-width="0" id="E8-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"/><path stroke-width="0" id="E8-MJMATHI-3C0" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"/><path stroke-width="0" id="E8-MJMAIN-22C5" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"/><path stroke-width="0" id="E8-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"/><path stroke-width="0" id="E8-MJMAIN-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"/><path stroke-width="0" id="E8-MJMAIN-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"/><path stroke-width="0" id="E8-MJMAIN-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"/><path stroke-width="0" id="E8-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E8-MJMAIN-32" x="0" y="0"/><use xlink:href="#E8-MJMATHI-3C0" x="500" y="0"/><use xlink:href="#E8-MJMAIN-22C5" x="1295" y="0"/><g transform="translate(1795,0)"><use xlink:href="#E8-MJMAIN-30"/><use xlink:href="#E8-MJMAIN-2E" x="500" y="0"/><use xlink:href="#E8-MJMAIN-30" x="778" y="0"/><use xlink:href="#E8-MJMAIN-34" x="1278" y="0"/></g><g transform="translate(3573,0)"><text font-family="STIXGeneral,'Arial Unicode MS',serif" stroke="none" transform="scale(61.362) matrix(1 0 0 -1 0 0)">Å</text><g transform="translate(681,408)"><use transform="scale(0.707)" xlink:href="#E8-MJMAIN-2212" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E8-MJMAIN-31" x="778" y="0"/></g></g></g></svg></span> .</p><p><img src="K-setting.png" width="80%" height="80%"/></p><p>生成KPOINTS的同时，<strong>会根据POSCAR中的元素类型从赝势库中提取并组合生成POTCAR</strong>，前提是你在<code>~/.vaspkit</code>里正确设置了<code>PBE_PATH</code>的路径，并根据<code>POTCAR_TYPE</code>选择是生成GGA-PW91、LDA还是PBE的赝势。值得注意的是提示信息<code>Written POTCAR File with the Recommended Potential!</code>，意味着<code>vaspkit</code>根据<a href="http://cms.mpi.univie.ac.at/vasp/vasp/Recommended_PAW_potentials_DFT_calculations_using_vasp_5_2.html">VASP官网的推荐</a>从PBE的赝势库中选择赝势。
PBE的赝势分为几种，无后缀、<code>_pv,_sv,_d</code> 和数字后缀，<code>_pv,_sv,_d</code> 就是说<code>semi-core</code>的<code>p,s</code>或者<code>d</code>也当做价态处理了。因为有些情况下，次外层电子也参与了成键。刘锦程提到进行<code>Bader</code>电荷分析，需要采用带<code>_pv,_sv</code>的赝势。特别地，官网提到<code>Important Note: If dimers with short bonds are present in the compound (O2 , CO, N2 , F2 , P2 , S2 , Cl2 ), we recommend to use the _h potentials. Specifically, C_h, O_h, N_h, F_h, P_h, S_h, Cl_h.</code>常用的做法是：用两种赝势测试一下对自己所关心的问题的影响情况。在影响不大的情况下，选用不含后缀的赝势，毕竟包含更多的价电子，截断能上升很多，计算量明显增大。</p><blockquote><p>如果需要手动生成POTCAR，可以通过功能<code>104</code><strong>手动选择每个元素的赝势类型</strong>。本例中演示给Zn选择<code>Zn_pv</code>的<code>PBE</code>赝势。选择功能<code>104</code>，依次输入需要设定的赝势类型<code>O</code>和<code>Zn_pv</code>，如果设定的赝势目录下没有你选择的赝势类型，将会提示你重新输入。</p></blockquote><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>6</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (1) Reading Structural Parameters from POSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Auto detected POTCAR_TYPE is O, please type the one you want!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">O</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Auto detected POTCAR_TYPE is Zn, please type the one you want!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Zn_pv</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (2) Written POTCAR File with user specified Potential!</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 120px;"/><div class="CodeMirror-gutters" style="height: 120px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>通过命令<code>grep TIT POTCAR</code>可以看到POTCAR中的赝势为<code>O</code>和<code>Zn_pv</code>，满足我们的需求。
为了取得有意义的结果，需要满足INCAR中的ENCUT大于POTCAR中的所有元素的ENMAX。通过以下命令可以查看所有元素的ENMAX：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-builtin">grep</span> ENMAX POTCAR</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>可以看到默认的INCAR参数中<code>ENCUT=400eV</code>被注释掉了，但是保留了<code>PREC   =  Normal</code>，程序会自动将<code>ENCUT</code>设为<code>max(ENMAX)</code>。当然也可以自行设置<code>ENCUT</code>参数，只要参数大于所有元素的<code>ENMAX</code>，这时候以自己设定的<code>ENCUT</code>参数为准。注意在优化晶胞常数时，需要用较高的<code>ENCUT</code>（<code>Learn VASP The Hard Way （Ex36）：直接优化晶格常数</code>），因此<code>LR</code>任务（优化晶格常数）模板生成的INCAR中默认设置了<code>PREC=High</code>，VASP程序会自动将<code>ENCUT</code>设为<code>max(ENMAX)*1.3</code>。乐平老师提到，为了确保相同体系的<code>ENCUT</code>一致，VASP最新的官方手册已经不推荐使用<code>PREC=High</code>了，它推荐设置为<code>PREC=Accurate</code>并手动设置<code>ENCUT</code>的值。
提交VASP计算任务，可以发现任务很快就失败了。错误日志如下：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>8</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> running on   16 total cores</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> distrk:  each k-point on   16 cores,    1 groups</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> distr:  one band on    1 cores,   16 groups</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> using from now: INCAR     </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> vasp.5.4.4.18Apr17-6-g9f103f2a35 (build Apr 07 2018 02:38:49) complex          </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> POSCAR found type information on POSCAR  O </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ERROR: the type information is not consistent with the number of types</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 160px;"/><div class="CodeMirror-gutters" style="height: 160px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><blockquote><p>通过分析发现，VASP只读出了O的元素和赝势，<em>Zn</em>没有从POSCAR中读出，因此报错。原因在于，从数据库下载的POSCAR中空格的分隔符是制表符<code>\t</code>，VASP不能正确读出以<code>\t</code>为分隔符的字符串。同样的问题也会在INCAR中出现。另外在WINDOWS系统下生成的POSCAR或INCAR在VASP中可能会出现非常奇怪的错误。最致命的是VASP<strong>不会自动检查POSCAR中的元素类型是否与POTCAR元素类型是否一致</strong>，也就是你算石墨烯也可以用H的赝势，并不会报错，但是结果一定是错的！因此<code>vaspkit 0.71</code>以后的版本加入了格式纠正和赝势元素检查的功能<code>109</code>。
输入<code>109</code>,<code>vaspkit</code>会自动进行INCAR和POSCAR的格式纠正，并检查赝势元素是否一致。</p></blockquote><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>5</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (1) Reading Structural Parameters from POSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> All Files Needed Exist.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Element type in POSCAR may be not corresponding to POTCAR</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> POTCAR:Zn_pv</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> POSCAR:Zn</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 100px;"/><div class="CodeMirror-gutters" style="height: 100px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>执行检查之后，再次提交任务。此时任务已经能正确运行。</p><blockquote><p>为了方便用户，在乐平老师的建议下，我们设置了功能<code>108</code>：<code>Successive procedure to generate VASP files and check</code>。先设置INCAR，再设置K点密度，生成KPOINTS和POTCAR，最后再调用功能<code>109</code>自动检查所有的文件是否存在问题。我们的目标是，<strong>VASP之前，先KIT一下</strong>。</p></blockquote><h4><a name="header-n101" class="md-header-anchor "/>3.2 能带计算</h4><p> 能带计算的KPOINTS与普通计算的KPOINTS不一样，通常需要第一布里渊区内的一条或几条高对称点路径来计算能带性质。  传统的做法是通过<a href="https://www.materialscloud.org/tools/seekpath/">SeeK-Path网站</a>或者Material Studio软件获得晶体倒易空间第一布里渊区内的高对称点，再通过脚本插值生成高对称点路径上的K点，得到满足要求的KPOINTS。好消息是新版的<code>vaspkit</code>集成了与SeeK-path一致的算法分析晶体的高对称点，可以方便地生成PBE泛函和HSE06杂化泛函所需的KPOINTS，<strong>目前不支持三斜晶系</strong>。
在<code>vaspkit.0.73/examples/hybrid_DFT_band</code>目录下有一个使用HSE06杂化泛函计算磷化镓的能带结构的例子。同样也可以使用PBE泛函计算该磷化镓结构的能带，只是普通的PBE泛函会低估带隙。为了计算能带，首先得获得晶体的第一布里渊区内的一条或几条高对称点路径。在有POSCAR的目录下运行<code>vaspkit</code>,输入<code>3</code>选择功能<code>Band-Path Generator</code>，在下一个界面输入<code>303</code>选择<code>3D bulk structure (Experimental)</code>，你会得到以下信息：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>36</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +-------------------------- Warm Tips --------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">         See An Example in vaspkit/examples/seek_kpath.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> This Feature Is Experimental & Check Your System using SeeK-Path.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> For More details See [www.materialscloud.org/work/tools/seekpath].</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (1) Reading Structural Parameters from POSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +-------------------------- Summary ----------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                           Prototype: AB</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">           Total Atoms in Input Cell:   2</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     Lattice Constants in Input Cell:   3.854   3.854   3.854</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">        Lattice Angles in Input Cell:  60.000  60.000  60.000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">       Total Atoms in Primitive Cell:   2</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Lattice Constants in Primitive Cell:   3.854   3.854   3.854</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    Lattice Angles in Primitive Cell:  60.000  60.000  60.000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                      Crystal System: Cubic</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                       Crystal Class: -43m</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                     Bravais Lattice: cF</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">18</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">            Extended Bravais Lattice: cF2</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">19</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                         Space Group: 216</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">20</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                         Point Group: 31 [ Td ]</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">21</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                       International: F-43m</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">22</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                 Symmetry Operations:  24</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">23</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                    Suggested K-Path: (shown in the next line)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">24</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> [ GAMMA-X-U|K-GAMMA-L-W-X ]</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">25</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">26</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (2) Written PRIMCELL.vasp file.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">27</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (3) Written KPATH.in File for Band-Structure Calculation.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">28</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (4) Written HIGH_SYMMETRY_POINTS File for Reference.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">29</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (5) Written POTCAR File with the Recommended Potential!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">30</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">31</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |                         * DISCLAIMER *                        |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">32</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |        CHECK Your Results for Consistency if Necessary        |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">33</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |   Bug Reports and Suggestions for Improvements Are Welcome    |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">34</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> | Citation of VASPKIT Is Not Mandatory BUT Would Be Appreciated |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">35</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |                     (^.^) GOOD LUCK (^.^)                     |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">36</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 720px;"/><div class="CodeMirror-gutters" style="height: 720px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p><code>vaspkit</code>会分析晶体的对称性并得到两条建议的能带路径<code>[ GAMMA-X-U|K-GAMMA-L-W-X ]</code>，同时生成了晶体的单胞结构<code>PRIMCELL.vasp</code>，并生成了<code>KPATH.in</code>用于能带结构计算。<code>KPATH.in</code>的第二行数字表示了每小段路径中插值的K点的数目，<strong><em>如果默认的数值都算不动的话，可以考虑将其设小</em></strong>。能带路径只针对于primitive cell，因此需要执行下面的命令，用生成的primitive cell作为计算的结构文件。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-builtin">cp</span> <span class="cm-attribute">-f</span> PRIMCELL.vasp POSCAR</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>下图展示的是磷化镓的primitive cell和其第一布里渊区的高对称点位置，由SeeK-path网站生成。
<img src="Brillouin_zone.png" alt="" referrerpolicy="no-referrer"/></p><h5><a name="header-n107" class="md-header-anchor "/>PBE泛函计算能带</h5><p>PBE泛函计算能带分为两步，第一步使用普通K点网格（功能102）进行自洽计算 ，启动<code>vaspkit</code>,输入<code>1</code>选择<code>VASP Input Files Generator</code>，再选择<code>108</code>选择<code>Successive Procedure to Generate VASP Files and Check</code>功能，输入<code>ST</code>,生成静态自洽的INCAR，并按照提示生成自洽用的K点。本例中<code>ISMEAR=0</code>，即<code>Gaussian Smearing</code>方法，如果是金属体系可以选择换成<code>ISMEAR=1</code>。接着调用VASP计算。第二步：<strong><em>使用KPATH.in里的高对称点信息作为新的KPOINTS，然后读入电荷CHGCAR</em></strong>进行能带非自洽计算，即：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>2</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-builtin">cp</span> <span class="cm-attribute">-f</span> KPATH.in KPOINTS</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-builtin">echo</span> <span class="cm-string">"ICHARG=11"</span> >> INCAR</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 40px;"/><div class="CodeMirror-gutters" style="height: 40px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>也就是读入上一步生成的CHGCAR并保持不变，调用VASP计算。
待第二步完成后，通过功能<code>21</code>从能量本征值文件中读入能带结构。<strong>值得一提的是，费米能级应该以自洽计算的为准</strong>，因此如果想获得准确的费米能级，可以在第一步运行之后执行以下命令提取自洽后DOSCAR中的费米能级给第二步处理能带数据用:</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-builtin">echo</span> <span class="cm-attribute">-e</span> <span class="cm-string">"\n"</span> <span class="cm-quote">$(sed -n 6p DOSCAR | awk '{print </span><span class="cm-def">$4</span><span class="cm-quote">}')</span> > FERMI_LEVEL.in</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><h5><a name="header-n113" class="md-header-anchor "/>HSE06杂化泛函计算能带</h5><p>杂化泛函相比于PBE泛函和DFT+U方法，在计算带隙方面很有优势，但是HSE06的杂化泛函需要KPOINTS里既有权重不为0的K点进行自洽计算，又要求有权重为0的高对称点计算能带性质。因此操作流程颇为繁琐。
重启<code>vaspkit</code>，输入<code>25</code>选择功能<code>Hybrid-DFT Band-Structure</code>，在下一个界面输入<code>251</code>选择<code>Generate KPOINTS File for Hybrid Band-Structure Calculation</code>。再输入<code>1</code>选择<code>Monkhorst-Pack Scheme</code>用MP方法生成自洽用的K点网格并根据建议输入<code>0.04</code>选择较密的K点密度（权重不为0的K点用于自恰计算），<strong>接下来还需手动指定能带路径上K点的密度，用于能带计算</strong>，再次输入<code>0.04</code>，即可生成HSE06杂化泛函所需的KPOINTS。0.72以前的版本在不同的能带路径上取相同的K点数，从而导致在不同路径上的K分布并不均匀，如下图a所示。<code>VASPKIT</code>最新版支持根据给定k点间隔<strong>自动确定不同能带路径上的K点数</strong>，从而保证在整个能带计算中<strong>均匀撒点</strong>，如下图b所示。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>17</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-operator">=======================</span> K-Mesh Scheme <span class="cm-operator">==========================</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-number">1</span>) Monkhorst-Pack Scheme                            </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-number">2</span>) Gamma Scheme                                     </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                                                     </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-number">0</span>)   Quit                                             </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-number">9</span>)   Back                                             </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">-------------</span>>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">1</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-operator">+</span><span class="cm-attribute">--------------------------</span> Warm Tips <span class="cm-attribute">--------------------------</span><span class="cm-operator">+</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Input Resolution Value to Determine K-Mesh <span class="cm-keyword">for</span> SCF Calculation: </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> (Typical Value: <span class="cm-number">0</span>.03-0.04 is Generally Precise Enough)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">------------</span>>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">0</span>.03</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Input Resolution Value along K-Path <span class="cm-keyword">for</span> Band Calculation: </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> (Typical Value: <span class="cm-number">0</span>.03 <span class="cm-keyword">for</span> DFT and <span class="cm-number">0</span>.04 <span class="cm-keyword">for</span> hybrid DFT)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">------------</span>>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">0</span>.04</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 340px;"/><div class="CodeMirror-gutters" style="height: 340px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p><img src="uniform_non-uniform.jpg" alt="" referrerpolicy="no-referrer"/></p><p>可通过KPOINTS文件第一行查看产生K点产生信息。<code>Parameters to Generate KPOINTS (Don't Edit This Line):  0.040 0.040 24 126 6 28 10 30 24 20 14</code>，第一个和第二个数据分别决定总能计算（权重不为零部分）和能带计算（权重为零部分）K点密度，也就是我们之前输入的数值，24表示总能计算部分在不可约布里渊区的K点数目，126表示能带计算中总K点数目，6表示共有6条能带路径，从第一到第六条能带上分别选取28,10,30,24,20和14个K点，共126个K点。<strong>此均匀撒点的方式能够提高能带的计算效率</strong>。但是<strong>请注意：由于0.72当前及之后版本将采用新的杂化能带计算KPOINTS文件格式，不再兼容由VASPKIT早期产生的杂化能带数据提取。</strong></p><p>因为HSE06计算非常耗时，因此本例中采用两步法加速收敛，当然也可以跳过第一步直接用HSE06进行自洽。第一步：使用PBE泛函产生波函数和电子密度，第二步：<strong><em>保持KPOINTS不变，读入波函数</em></strong>进行HSE06计算。
利用功能<code>Customize INCAR File</code>生成第一步PBE自洽需要的INCR。重启<code>vaspkit</code>,输入<code>1</code>选择<code>VASP Input Files Generator</code>，再选择<code>101</code>选择<code>Customize INCAR File</code>功能，输入<code>ST</code>,生成静态自洽的INCAR。本例中<code>ISMEAR=0</code>，即<code>Gaussian Smearing</code>方法，如果是金属体系可以选择换成<code>ISMEAR=1</code>。调用VASP计算，待自洽完成后执行第二步HSE06计算。重启<code>vaspkit</code>, 选择功能<code>101 Customize INCAR File</code>功能，输入<code>STH6</code>,生成HSE06计算所需要的INCAR。再次调用VASP计算后，就完成了HSE06的自洽计算。
接下来使用<code>vaspkit</code>提取能带数据，并输出高对称点在能带图中的坐标信息。输入<code>25</code>选择功能<code>Hybrid-DFT Band-Structure</code>，在下一个界面输入<code>252</code>选择<code>Read Band-Structure for Hybrid-DFT Calculation</code>处理能带数据。处理结果如下所示</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>9</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (1) Reading Input Parameters From INCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (2) Reading Fermi-Level From DOSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (3) Reading Energy-Levels From EIGENVAL File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (4) Reading Lattices & Atomic-Positions from POSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (5) Reading K-Paths From KPATH.in File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (6) Written BAND.dat File!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (7) Written BAND-REFORMATTED.dat File!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (8) Written KLINES.dat File!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (9) Written KLABELS File!</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 180px;"/><div class="CodeMirror-gutters" style="height: 180px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p><code>BAND-REFORMATTED.dat</code>是修改后生成的能带信息（<strong>0.70版本生成的有问题，Band.dat正常！0.71以后的版本以后已修复。</strong>），格式如下所示，第一列是K-PATH，相邻的距离为高对称点在倒空间的距离，第二列，第三列等即为所需的不同的能带线。如果开了自旋，第二列和第三列为能带1的spin up和spin down，以此类推。将dat文件拖入Origin软件后，即可得到能带图。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>9</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"># Kpath    Energy-Level (in eV)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">       0.00000     -14.54063      -0.82009      -0.82009 </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">       0.12809     -14.48597      -1.24459      -0.97903 </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">       0.25617     -14.32291      -2.13627      -1.37615 </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">       0.38426     -14.05442      -3.15793      -1.87258 </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">       0.51234     -13.68641      -4.20790      -2.37100 </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">       0.64043     -13.22973      -5.24586      -2.81765 </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">       0.76851     -12.70500      -6.23748      -3.18362 </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">       0.89660     -12.15541      -7.12954      -3.45312 </span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 180px;"/><div class="CodeMirror-gutters" style="height: 180px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p><code>KLABELS</code>是由读取能带标识的子模块生成的。通过读取<code>KPATH.in</code>（PBE能带计算时为KPOINTS）高对称点后标识，写入KLABELS文件。
<code>KPATH.in</code>文件内容如下：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>21</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Generated by VASPKIT based on Hinuma et al.'s Paper, Comp. Mat. Sci. 128, 140 (2017), DOI: 10.1016/j.commatsci.2016.10.015.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   10</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Line-Mode</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Reciprocal</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.0000000000   0.0000000000   0.0000000000     GAMMA          </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.5000000000   0.0000000000   0.5000000000     X              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.5000000000   0.0000000000   0.5000000000     X              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.6250000000   0.2500000000   0.6250000000     U              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.3750000000   0.3750000000   0.7500000000     K              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.0000000000   0.0000000000   0.0000000000     GAMMA          </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.0000000000   0.0000000000   0.0000000000     GAMMA          </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.5000000000   0.5000000000   0.5000000000     L              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.5000000000   0.5000000000   0.5000000000     L              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">18</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.5000000000   0.2500000000   0.7500000000     W              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">19</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">20</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.5000000000   0.2500000000   0.7500000000     W              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">21</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.5000000000   0.0000000000   0.5000000000     X   </span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 440px;"/><div class="CodeMirror-gutters" style="height: 440px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p><code>KLABELS</code>文件如下：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>9</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">K-Label    K-Coordinate in band-structure plots </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">GAMMA              0.000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">X                  1.153</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">U|K                1.560</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">GAMMA              2.783</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">L                  3.781</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">W                  4.597</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">X                  5.173</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">* Give the label for each high symmetry point in KPOINTS (KPATH.in) file. Otherwise, they will be identified as 'Undefined' in KLABELS file</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 200px;"/><div class="CodeMirror-gutters" style="height: 200px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>因为路径分了两条，所以能带图中第二个高对称点位置的标识为<code>U|K</code>。<code>K-Coordinate in band-structure plots</code>也就是每个高对称点在能带图中的横坐标位置。例如能带路径<code>W-L-Gamma</code>, <code>Gamma</code>的横坐标就是<code>|W-L|+|L-Gamma|</code>两条线段（在倒空间中的）长度的累加，以此类推。当出现第二条路径<code>X-W</code>，<code>Gamma|X</code>点的横坐标就是第一条路径末点<code>Gamma</code>的横坐标，而<code>W</code>点的横坐标为<code>Gamma|X</code>点的横坐标加上<code>|X-W|</code>的线段长度。
用户在Origin软件中处理了<code>BAND-REFORMATTED.dat</code>后，需要按照<code>KLABELS</code>文件中的位置在能带图中标识高对称点位置。</p><p><code>vaspkit0.73</code>版本之后支持<strong>自动绘制能带图和DOS图</strong>，并能够进行自定义设置。当然如果要绘制出出版级的图片，需要自己对生成的Python绘图脚本进行设置。绘图需要用户安装了<code>Python解释器</code>，并安装<code>Numpy</code>和<code>Matplotlib</code>库。在<code>~/.vaspkit</code>环境变量中进行以下设置：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>2</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">PYTHON_PATH              /usr/bin/python    <span class="cm-comment">#  Python exe containing numpy and matplotlib</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">PLOT_MATPLOTLIB          .TRUE.            <span class="cm-comment">#  Set it .TRUE. if you want to generate Graphs. (Matplotlib and Numpy packages MUST be embedded in Python)</span></span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 80px;"/><div class="CodeMirror-gutters" style="height: 80px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>在运行提取能带或者DOS时会自动进行绘图，选择<code>0</code>会自动根据预设的绘图设置进行绘图（下图的能带图即使用默认的设置绘的图），亦可选择<code>1</code>进行手动调整。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">If you want use the default setting, type <span class="cm-number">0</span>, <span class="cm-keyword">if</span> modity type <span class="cm-number">1</span></span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>可以更改的选项有图片尺寸，图片分辨率，能量选择范围，线宽，字体，及颜色，字体大小等。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>7</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-operator">============================</span> change_plot_setup <span class="cm-operator">========================</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-number">1</span>) Set <span class="cm-keyword">if</span> show a graph window or generate graphs silently</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-number">2</span>) Set Figure size</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-number">3</span>) Set Figure DPI</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-number">4</span>) Set energy ranges <span class="cm-keyword">for</span> DOS or Band</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-number">5</span>) Set <span class="cm-keyword">if</span> use the default line colors <span class="cm-keyword">set</span> or linewidth</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-number">6</span>) Set fontsize,font-family,fontcolor</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 140px;"/><div class="CodeMirror-gutters" style="height: 140px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p> </p> <div align="center"><img src="./HSEband.png" width="80%" height="80%" onerror="this.style.display = 'none';"/></div><h4><a name="header-n135" class="md-header-anchor "/>3.3 分波态密度和局域态密度</h4><blockquote><p>原则上讲，<a href="http://www.cailiaoniu.com/51344.html">态密度可以作为能带结构的一个可视化结果</a>。很多分析和能带的分析结果可以一一对应，很多术语也和能带分析相通。但是因为它更直观，因此在结果讨论中用得比能带分析更广泛一些。在电子能级为准连续分布的情况下，单位能量间隔内的电子态数目。即能量介于<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.774ex" height="1.909ex" viewbox="0 -751.8 764 821.9" role="img" focusable="false" style="vertical-align: -0.163ex;"><defs><path stroke-width="0" id="E9-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E9-MJMATHI-45" x="0" y="0"/></g></svg></span> ~<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="8.323ex" height="2.384ex" viewbox="0 -819.9 3583.4 1026.4" role="img" focusable="false" style="vertical-align: -0.48ex;"><defs><path stroke-width="0" id="E10-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"/><path stroke-width="0" id="E10-MJMAIN-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"/><path stroke-width="0" id="E10-MJMAIN-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E10-MJMATHI-45" x="0" y="0"/><use xlink:href="#E10-MJMAIN-2B" x="986" y="0"/><use xlink:href="#E10-MJMAIN-394" x="1986" y="0"/><use xlink:href="#E10-MJMATHI-45" x="2819" y="0"/></g></svg></span> 之间的量子态数目<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.614ex" height="2.067ex" viewbox="0 -819.9 1556 890.1" role="img" focusable="false" style="vertical-align: -0.163ex;"><defs><path stroke-width="0" id="E11-MJMAIN-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"/><path stroke-width="0" id="E11-MJMATHI-5A" d="M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E11-MJMAIN-394" x="0" y="0"/><use xlink:href="#E11-MJMATHI-5A" x="833" y="0"/></g></svg></span> 与能量差<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.709ex" height="2.067ex" viewbox="0 -819.9 1597 890.1" role="img" focusable="false" style="vertical-align: -0.163ex;"><defs><path stroke-width="0" id="E12-MJMAIN-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"/><path stroke-width="0" id="E12-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E12-MJMAIN-394" x="0" y="0"/><use xlink:href="#E12-MJMATHI-45" x="833" y="0"/></g></svg></span> 之比，即为态密度。能态密度与能带结构密切相关，是一个重要的基本函数。固体的许多特性，如电子比热、光和X射线的吸收和发射等，都与能态密度有关。在VASP中，<code>LORBIT=10</code>计算的就是LDOS，也就是每个原子的<a href="http://blog.sciencenet.cn/blog-316926-493110.html">局域态密度</a> (local DOS)，是分解到每个原子上面的s,p,d；<code>LORBIT=11</code>，计算的就是PDOS,投影态密度(projected DOS)或分波态密度(partial DOS)，不仅分解到每个原子的s,p,d,而且还进行px,py,pz分解。</p></blockquote><p><code>vaspkit</code>最近优化了DOS的提取功能。参考了李强的脚本 。相对于<code>P4VASP</code>提取DOS信息，<code>vaspkit</code>有以下几个优点：①不需要将体积庞大的<code>vasprun.xml</code>拖回本地；②支持f轨道的提取，<code>P4VASP</code>提取f轨道时存在bug；③生成的<code>dat</code>文件格式友好，而<code>P4VASP</code>导出的<code>dat</code>是以空格为分隔符，无法直接用Origin绘图，并且没有DOS线的图例。</p><p>以官网的<a href="http://cms.mpi.univie.ac.at/wiki/index.php/Partial_DOS_of_CO_on_Ni_111_surface">CO在Ni表面的吸附模型</a>和<a href="http://cms.mpi.univie.ac.at/wiki/index.php/Ni_100_surface_DOS">Ni 100 surface</a>为例提取 PDOS。也可在大师兄群里(<code>217821116</code>)下载到<code>VASP Official Tutorials.pdf</code></p><p>CO吸附的例子中设置了<code>LORBIT=11</code>投影了轨道,关闭了自旋极化。</p><p>在<code>/vaspkit.0.73/examples/LDOS_PDOS/Partial_DOS_of_CO_on_Ni_111_surface</code>目录下启动<code>vaspkit</code>，输入命令<code>115</code>选择子功能<code>The Sum of Projected DOS for Selected Atoms and orbitals</code>。我们需要提取的是<code>O</code>的<code>s，p</code>轨道，<code>C</code>的<code>s，p</code>轨道以及表面的<code>dxy</code>和<code>d3z2-r2(dz2)</code>轨道。首先提示你选择元素（累加），第一次输入元素<code>O</code>，回车后提示你输入提取的轨道名（累加），第一次输入轨道<code>s</code>。回车后重复以上两个操作。如果想结束输入，在<strong>元素选择行</strong>直接按<strong>回车键</strong>结束输入。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>9</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Input the Symbol and/or Number of Atoms to Sum [Total-atom: <span class="cm-number">7</span>]</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> (Free Format is OK, e.g., C Fe H <span class="cm-number">1</span><span class="cm-attribute">-4</span> <span class="cm-number">7</span> <span class="cm-number">8</span> <span class="cm-number">24</span>),Press <span class="cm-string">"Enter"</span> <span class="cm-keyword">if</span> you want to end e</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ntry!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">------------</span>>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">O</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Input the Orbitals to Sum</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Which orbital? s py pz px dxy dyz dz2 dxz dx2 f-3 ~ f3, <span class="cm-string">"all"</span> <span class="cm-keyword">for</span> summing ALL.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">s</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 180px;"/><div class="CodeMirror-gutters" style="height: 180px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>本次的输入内容如下：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">O <span class="cm-attribute">-</span> s <span class="cm-attribute">-</span> O <span class="cm-attribute">-</span> p <span class="cm-attribute">-</span> C <span class="cm-attribute">-</span> s <span class="cm-attribute">-</span> C <span class="cm-attribute">-</span> p <span class="cm-attribute">-</span> Ni <span class="cm-attribute">-</span> dxy <span class="cm-attribute">-</span> Ni <span class="cm-attribute">-</span> dz2 <span class="cm-attribute">-</span> <span class="cm-string">'Enter'</span></span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>在目录下会生成一个<code>PDOS_USER.dat</code>，内容如下：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>5</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    <span class="cm-comment">#Energy        O_s        O_p        C_s        C_p     Ni_dxy    Ni_dz2</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  <span class="cm-attribute">-27</span>.10266    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  <span class="cm-attribute">-26</span>.92966    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  <span class="cm-attribute">-26</span>.75566    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  <span class="cm-attribute">-26</span>.58266    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000    <span class="cm-number">0</span>.00000</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 100px;"/><div class="CodeMirror-gutters" style="height: 100px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>第一行是列名，也就是轨道的名称，2-301行为PDOS的数据点。拖入Origin可以得到PDOS图，官网的图也放在下面供参考。在<code>~/.vaspkit</code>中打开绘图设置后，<code>vaspkit</code>会自动绘制<code>PDOS</code>图。VASP5.4.4<code>计算的O的s轨道的PDOS会比官网例子低一点，此现象已经用</code>P4VASP`验证无误。</p><p><img src="DOS_plot.png" alt="" referrerpolicy="no-referrer"/></p><p>元素行接受<strong>自由格式</strong>输入，你可以输入以下内容<code>1-3 4 Ni</code>表示选择元素1,2,3,4和Ni元素的PDOS进行累加。轨道行只支持标准输入，如果使用了<code>LORBIT=10</code>不投影轨道，你只能选择 <code>s p d f</code>中的一个或多个，如果使用了<code>LORBIT=11</code>投影了轨道，你可以从<code>s p d f</code>和<code>s py pz px dxy dyz dz2 dxz dx2 f-3 f-2 f-1 f0 f1 f2 f3</code>中选择一个或多个输入。轨道行还支持输入<code>all</code>计算所有轨道的DOS之和。</p><p>比如元素行输入<code>C O</code> ,对应的轨道选择<code>s px</code>，那么提取的就是所有C和O元素的<code>s</code>轨道和<code>px</code>轨道的PDOS之和。 <code>PDOS_USER.dat</code>中的轨道名 为<code>#Energy    C&O_s&px</code>，显而易懂。</p><p>接下来以纯的Ni表面为例。<code>vaspkit.0.73/examples/LDOS_PDOS/Ni_100_surface_DOS</code></p><p>本例设置了<code>LORBIT=10</code>,开启了自旋极化。</p><p>本次的输入内容如下：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">1</span> <span class="cm-number">5</span> <span class="cm-attribute">-</span> all <span class="cm-attribute">-</span> <span class="cm-number">3</span> <span class="cm-attribute">-</span> all <span class="cm-attribute">-</span> <span class="cm-string">'Enter'</span></span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>提取的是上下Ni表面的总态密度和中间<code>bulk</code>层的总态密度。</p><p><code>PDOS_USER.dat</code>的内容如下：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>4</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     <span class="cm-comment">#Energy  up_1&5_all  dw_1&5_all    up_3_all    dw_3_all</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-attribute">-10</span>.54087     <span class="cm-number">0</span>.00000     <span class="cm-number">0</span>.00000     <span class="cm-number">0</span>.00000     <span class="cm-number">0</span>.00000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-attribute">-10</span>.42787     <span class="cm-number">0</span>.00000     <span class="cm-number">0</span>.00000     <span class="cm-number">0</span>.00000     <span class="cm-number">0</span>.00000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-attribute">-10</span>.31487     <span class="cm-number">0</span>.00000     <span class="cm-number">0</span>.00000     <span class="cm-number">0</span>.00000     <span class="cm-number">0</span>.00000</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 80px;"/><div class="CodeMirror-gutters" style="height: 80px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>第二列为上下表面的<code>spin up</code>的总态密度，第三列为上下表面的<code>spin down</code>的总态密度。拖进<code>Origin</code>，可以轻松做出 DOS图。</p> <div align="center"><img src="DOS_Ni.jpg" width="50%" height="50%" onerror="this.style.display = 'none';"/></div><h4><a name="header-n160" class="md-header-anchor "/>3.4 热力学量校正</h4><p>众所周知，<code>VASP</code>计算的是在体系在0K下的电子能量，没有考虑温度的贡献。做电化学模拟或者计算反应速率时需要计算自由能， 为了获得反应热需要计算焓， 为了获得0K下的体系内能要计算ZPE。<code>Learn VASP The Hard Way （Ex69） 表面吸附物种熵的计算</code>中讲述了气相分子和吸附质分子熵不同的计算方法,该系列教程可以在群<code>217821116</code>下载到PDF版本。刘锦程发布了两篇比较详细的自由能校正教程，包括<a href="https://mp.weixin.qq.com/s/2nCcf1VXDfSti17127qvjA">气体分子自由能</a>和<a href="https://mp.weixin.qq.com/s/PYZs2ggrp4Jh6STZqr1hxg">吸附分子自由能</a>，可以参考。</p><blockquote><p>对一个体系来说，焓、熵可以通过统计热力学计算分子的配分函数来获取：主要考虑理想气体的平动，转动，振动，电子贡献。对分子来说，举个例子，一个非线性的三原子分子，一共有3N个自由度。气相里面为：3个平动，3个转动以及3N-6个振动。但是当它吸附到表面上，由于平动和转动被限制住了，这6个自由度则会转化成振动自由度，也就是在表面上分子有3N个振动模式。如果你可视化表面上吸附分子频率计算的结果，会发现最后6个应的是平动和转动，但它们已经不是气相中的平动和转动了，我们称之为：frustrated translation，frustrated rotation。</p></blockquote><h5><a name="header-n164" class="md-header-anchor "/>气相分子的热力学校正</h5><p>李强的教程<code>Learn VASP The Hard Way （Ex68） 频率，零点能，吉布斯自由能的计算</code>提到VASP对于温度校正做的实在是太差了，他建议通过查询数据库（NIST等）的方法获得气相分子的热力学量。 而<code>Gaussian</code>对于分子和团簇的热力学校正功能比较完善。<code>Sobereva</code>开发了一个实用意义也有教学意义的<code>Shermo</code>程序（<code>http://sobereva.com/315</code>），通过分析高斯的输出结果，计算平动、转动、振动和电子贡献，得到给定温度、压力下体系的内能、焓、熵、自由能、热容。建议大家先看一下该程序的文档。<code>VASPKIT</code>将该程序集成进来，用户可以直接根据VASP的振动结果给出气相分子的内能、焓、熵、自由能校正。
下面以乙醇（/examples/thermo_correction/ethanol）为例对比VASP和Gaussian的热力学校正结果。
振动计算完成后，启动<code>VASPKIT</code>,输入<code>5</code>选择功能<code>Catalysis-ElectroChem Kit</code>，在下一个界面输入<code>502</code>选择<code>Thermal corrections for Gas</code>。紧接着提示输入温度<code>298.15K</code>、压力<code>1atm</code>和自旋多重度<code>1</code>。自旋多重度定义为2S+1，其中S是自旋角动量，它与体系内的单电子数(N)相关。S=N/2，所以说到底最简单的判断方法：自旋多重度等于单电子数+1。乙醇没有单电子，因此自旋多重度为1。（氧气的自旋多重度为3.）<strong>该模块需要所有的原子都放开，也就是不能有原子被固定。</strong></p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>17</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +-------------------------- Warm Tips --------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">        This Feature Was Contributed by Nan XU, Sobereva.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   See An Example in vaspkit/examples/thermo_correction/ethanol.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Vibrations ,Translation,Rotation,Electron contributions are considered.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> GAS molecules should not be with any fix.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (1) Reading Structural Parameters from CONTCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (2) Analyze Molecular symmetry information...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Molecular symmetry is: Cs</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Please input Temperature(K)!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">298.15</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Please input Pressure(Atm)!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">1</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Please input Spin multiplicity!--(Number of Unpaired electron + 1)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">1</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ------------>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 340px;"/><div class="CodeMirror-gutters" style="height: 340px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p><code>VASPKIT</code>会计算调用<code>Shermo</code>模块计算热力学贡献量。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>9</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (3) Extracting frequencies from OUTCAR...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (4) Reading OUTCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (5) Calculate Thermal Corrections...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Zero-point energy E_ZPE   :      48.501 kcal/mol    2.103130 eV</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Thermal correction to U(T):      51.486 kcal/mol    2.232567 eV</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Thermal correction to H(T):      52.078 kcal/mol    2.258259 eV</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Thermal correction to G(T):      31.891 kcal/mol    1.382881 eV</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Thanks to Sobereva!(sobereva@sina.com)</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 180px;"/><div class="CodeMirror-gutters" style="height: 180px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>而高斯<code>G09RevD.01</code>的计算结果为<code>U(T) 51.94 kcal/mol， H(T) 52.53  kcal/mol， G(T) 33.67 kcal/mol</code>，理论水平为<code>B3LYP/CC-pVDZ</code>，可以看到使用VASPKIT计算的分子热力学校正量已经接近Gaussian的计算结果。</p><h5><a name="header-n171" class="md-header-anchor "/>吸附质分子的热力学校正</h5><p>对于吸附质分子，<code>Learn VASP The Hard Way （Ex69） 表面吸附物种熵的计算</code>建议忽略frustrated的平动和转动和电子贡献，只考虑3N-6的振动部分。本模块的原理正是基于此教程,由许楠、李强和刘锦程贡献。<strong>注意：该模块不能计算气相分子的热力学贡献。</strong>
以/vaspkit.0.73/examples/thermo_correction/ORR为例。下图展示的是在氧气在磷掺杂的石墨烯上的解离吸附的过渡态（Carbon, 2016, 105:214-223.），图片用VESTA软件可视化。为了求得温度的贡献，需要进行振动分析(<code>IBRION=5</code>),为了节省计算资源，只有P、O原子放开，而C原子固定住，在计算Energy Profile时，需要对其他体系做振动分析，保持放开的原子一致。<strong>值得注意的是，本模块只考虑的振动的贡献，而电子的贡献忽略了，将波数小于50cm-1 的 frustrated translation，frustrated rotation的受限振动部分调节为50cm-1 的振动计入对熵的贡献。</strong></p>  <div align="center"><img src="ORR.jpg" width="65%" height="65%" onerror="this.style.display = 'none';"/></div><p>启动<code>vaspkit</code>,输入<code>5</code>选择功能<code>Catalysis-ElectroChem Kit</code>，在下一个界面输入<code>501</code>选择<code>Thermal corrections for Adsorbate</code>。紧接着提示<code>Please Enter The Temperature (K):</code>，输入常温298.15K，屏幕会输出以下信息：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>23</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +-------------------------- Warm Tips --------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> This Feature Was Contributed by Nan XU, Qiang LI and Jincheng LIU.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     See An Example in vaspkit/examples/thermo_correction/ORR.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Only vibrations! No Translation & Rotation & Electron contribitions.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Please Enter The Temperature (K):</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ------------>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">298.15</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (1) Reading OUTCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +-------------------------- Summary ----------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> H = E_DFT + E_ZPE + E_H</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> G = H - TS = E_DFT + E_ZPE + E_H - T*S</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Temperature (K): 298.1</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Entropy (eV/K):  0.0005</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">18</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Entropy contribution T*S (eV):  0.1541</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">19</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Enthalpy contribution E_H (eV):  0.0858</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">20</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Zero-point energy E_ZPE (eV):  0.1944</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">21</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Thermal correction to G(T) (eV):  0.1261</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">22</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Total energy at Zero K (eV) :   -159.3511</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">23</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Gibbs free energy at 298.1 K (eV) :   -159.2250</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 460px;"/><div class="CodeMirror-gutters" style="height: 460px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>298.15K下体系的吉布斯自由能由以下公式给定：</p><blockquote><p>H = E_DFT + E_ZPE + E_H 
G = H - TS = E_DFT + E_ZPE + E_H - T*S  <br/>E_DFT为体系在0K下的静态电子能量。本例中体系在298.15下的自由能为-159.2250 eV。要记住的是DFT计算中绝对能量没有意义，只有相对能量才make sense。</p></blockquote><p><strong>需要指出的是，0.70版读取的Total energy at Zero K (eV)存在一个bug，0.71以后版本已修复。</strong></p><p> </p><h4><a name="header-n181" class="md-header-anchor "/>3.5 差分电荷密度图的绘制</h4><p>差分电荷密度用来查看成键前后电荷的重新分布。这里以小木虫上的一个<a href="http://muchong.com/html/201006/2129228.html">CO差分电荷</a>为例。</p><blockquote><p>文献中常用的差分电荷密度图为二次差分电荷密度图(difference charge density)，区别于差分电荷密度图(deformation charge density)。 差分电荷定义为成键后的电荷密度与对应的点的原子电荷密度之差。通过差分电荷密度的计算和分析，可以清楚地得到在成键和成键电子耦合过程中的电荷移动以及成键极化方向等性质。 “二次”是指同一个体系化学成分或者几何构型改变之后电荷的重新分布。
Deformation charge density 的公式定义为 </p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n185" cid="n185" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="134.063px" height="18.0556px" viewbox="0 -819.9 9135.9 1230.9" role="img" focusable="false" style="vertical-align: -0.955ex; max-width: 100%;"><defs><path stroke-width="0" id="E1-MJMAIN-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"/><path stroke-width="0" id="E1-MJMATHI-3C1" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 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transform="translate(6152,0)"><use xlink:href="#E1-MJMATHI-3C1" x="0" y="0"/><g transform="translate(517,-162)"><use transform="scale(0.707)" xlink:href="#E1-MJMATHI-41" x="0" y="0"/><g transform="translate(530,0)"><use transform="scale(0.707)" xlink:href="#E1-MJMATHI-42" x="0" y="0"/><g transform="translate(536,-107)"><use transform="scale(0.545)" xlink:href="#E1-MJMATHI-61" x="0" y="0"/><use transform="scale(0.545)" xlink:href="#E1-MJMATHI-74" x="529" y="0"/><use transform="scale(0.545)" xlink:href="#E1-MJMATHI-6F" x="890" y="0"/><use transform="scale(0.545)" xlink:href="#E1-MJMATHI-6D" x="1375" y="0"/></g></g></g></g></g></svg></span></div></div></div><p>Difference charge density的公式定义为 </p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n187" cid="n187" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-2-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="133.733px" height="17.066px" viewbox="0 -819.9 9113.5 1162.7" role="img" focusable="false" style="vertical-align: -0.796ex; max-width: 100%;"><defs><path stroke-width="0" id="E2-MJMAIN-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"/><path stroke-width="0" id="E2-MJMATHI-3C1" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"/><path stroke-width="0" id="E2-MJMAIN-3D" d="M56 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45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z"/><path stroke-width="0" id="E2-MJMAIN-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E2-MJMAIN-394" x="0" y="0"/><use xlink:href="#E2-MJMATHI-3C1" x="833" y="0"/><use xlink:href="#E2-MJMAIN-3D" x="1627" y="0"/><g transform="translate(2683,0)"><use xlink:href="#E2-MJMATHI-3C1" x="0" y="0"/><g transform="translate(517,-162)"><use transform="scale(0.707)" xlink:href="#E2-MJMATHI-41" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E2-MJMATHI-42" x="750" y="0"/></g></g><use xlink:href="#E2-MJMAIN-2212" x="4589" y="0"/><g transform="translate(5590,0)"><use xlink:href="#E2-MJMATHI-3C1" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E2-MJMATHI-41" x="731" y="-229"/></g><use xlink:href="#E2-MJMAIN-2212" x="6959" y="0"/><g transform="translate(7959,0)"><use xlink:href="#E2-MJMATHI-3C1" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E2-MJMATHI-42" x="731" y="-213"/></g></g></svg></span></div></div></div></blockquote><p>计算Deformation charge density时，<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.123ex" height="2.147ex" viewbox="0 -554.3 2205.7 924.4" role="img" focusable="false" style="vertical-align: -0.86ex;"><defs><path stroke-width="0" id="E13-MJMATHI-3C1" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"/><path stroke-width="0" id="E13-MJMATHI-41" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"/><path stroke-width="0" id="E13-MJMATHI-42" d="M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z"/><path stroke-width="0" id="E13-MJMATHI-73" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"/><path stroke-width="0" id="E13-MJMATHI-63" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E13-MJMATHI-3C1" x="0" y="0"/><g transform="translate(517,-162)"><use transform="scale(0.707)" xlink:href="#E13-MJMATHI-41" x="0" y="0"/><g transform="translate(530,0)"><use transform="scale(0.707)" xlink:href="#E13-MJMATHI-42" x="0" y="0"/><g transform="translate(536,-107)"><use transform="scale(0.5)" xlink:href="#E13-MJMATHI-73" x="0" y="0"/><use transform="scale(0.5)" xlink:href="#E13-MJMATHI-63" x="469" y="0"/></g></g></g></g></svg></span> 可由自洽计算的CHG或CHGCAR得到,而<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.692ex" height="2.147ex" viewbox="0 -554.3 2881.2 924.4" role="img" focusable="false" style="vertical-align: -0.86ex;"><defs><path stroke-width="0" id="E14-MJMATHI-3C1" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"/><path stroke-width="0" id="E14-MJMATHI-41" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"/><path stroke-width="0" id="E14-MJMATHI-42" d="M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z"/><path stroke-width="0" id="E14-MJMATHI-61" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"/><path stroke-width="0" id="E14-MJMATHI-74" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"/><path stroke-width="0" id="E14-MJMATHI-6F" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"/><path stroke-width="0" id="E14-MJMATHI-6D" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E14-MJMATHI-3C1" x="0" y="0"/><g transform="translate(517,-162)"><use transform="scale(0.707)" xlink:href="#E14-MJMATHI-41" x="0" y="0"/><g transform="translate(530,0)"><use transform="scale(0.707)" xlink:href="#E14-MJMATHI-42" x="0" y="0"/><g transform="translate(536,-107)"><use transform="scale(0.5)" xlink:href="#E14-MJMATHI-61" x="0" y="0"/><use transform="scale(0.5)" xlink:href="#E14-MJMATHI-74" x="529" y="0"/><use transform="scale(0.5)" xlink:href="#E14-MJMATHI-6F" x="890" y="0"/><use transform="scale(0.5)" xlink:href="#E14-MJMATHI-6D" x="1375" y="0"/></g></g></g></g></svg></span> 所需的 CHG 或 CHGCAR 可由下述非自洽计算得到:仍使用自洽计算的四个输入文件，但INCAR中需要设置<code>ICHARG=12 和 NELM=0</code>，<a href="http://blog.sciencenet.cn/blog-567091-736154.html">也就是CHGCAR是由孤立原子电荷的简单叠加构成</a>。
而Difference charge density是文献中最常用的方法，需要对三个不同结构(A,B,AB)做自洽计算。步骤如下：</p><ul><li>对优化后的结构做静态自洽计算
要注意的是，AB、A和B要分别放在同样大小的空间格子中并保证A和B与AB中相应坐标不变，<strong>计算时也要保证三次自洽计算所采用的FFT mesh 一致（NGXF,NGYF,NGZF）</strong>。
     INCAR中几个注意的参数：
       <code>IBRION = -1;NSW = 0;NGXF,NGYF,NGZF</code></li><li>利用<code>vaspkit</code>对三个结构的CHGCAR做差
    根据公式<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="21.213ex" height="2.575ex" viewbox="0 -799.7 9133.3 1108.5" role="img" focusable="false" style="vertical-align: -0.717ex;"><defs><path stroke-width="0" id="E15-MJMAIN-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"/><path stroke-width="0" id="E15-MJMATHI-3C1" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"/><path stroke-width="0" id="E15-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"/><path stroke-width="0" id="E15-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"/><path stroke-width="0" id="E15-MJMATHI-4F" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"/><path stroke-width="0" id="E15-MJMAIN-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E15-MJMAIN-394" x="0" y="0"/><use xlink:href="#E15-MJMATHI-3C1" x="833" y="0"/><use xlink:href="#E15-MJMAIN-3D" x="1627" y="0"/><g transform="translate(2683,0)"><use xlink:href="#E15-MJMATHI-3C1" x="0" y="0"/><g transform="translate(517,-155)"><use transform="scale(0.707)" xlink:href="#E15-MJMATHI-43" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E15-MJMATHI-4F" x="760" y="0"/></g></g><use xlink:href="#E15-MJMAIN-2212" x="4599" y="0"/><g transform="translate(5599,0)"><use xlink:href="#E15-MJMATHI-3C1" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E15-MJMATHI-4F" x="731" y="-217"/></g><use xlink:href="#E15-MJMAIN-2212" x="6978" y="0"/><g transform="translate(7978,0)"><use xlink:href="#E15-MJMATHI-3C1" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E15-MJMATHI-43" x="731" y="-218"/></g></g></svg></span> ，我们需要将CO的CHGCAR减去O的，再减去C的，就能得到想要的二次差分电荷密度。在父目录下启动<code>vaspkit</code>，输入<code>34</code>，选择功能<code>Charge & Spin Density</code>，进入电荷密度子菜单，再输入命令<code>314</code>选择<code>Charge-Density Difference</code>，在下一个界面提示输入<code>CO/CHGCAR C/CHGCAR O/CHGCAR</code>，会显示以下信息：</li></ul><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>14</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ======================= File Options ============================</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Input the Names of Charge/Potential Files with Space:</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> (Tip: To get AB-A-B, type: ~/AB/CHGCAR ./A/CHGCAR ../B/CHGCAR)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ------------>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">CO/CHGCAR C/CHGCAR O/CHGCAR</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (1) Reading Structural Parameters from CO/CHGCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (2) Reading Charge Density From CO/CHGCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (3) Reading Structural Parameters from C/CHGCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (4) Reading Charge Density From C/CHGCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (5) Reading Structural Parameters from O/CHGCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (6) Reading Charge Density From O/CHGCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> (7) Written CHGDIFF.vasp File!</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 280px;"/><div class="CodeMirror-gutters" style="height: 280px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p><strong>此版本不需对路径加引号</strong>。运行完后，会在当前目录下生成<code>CHGDIFF.vasp</code>，即为CO的电荷密度差。用VESTA软件可视化如下，黄色部分表示电荷密度增加，蓝色表示电荷密度减少：</p><p><img src="chgdiff.jpg" width="50%" height="50%"/></p><p>通过组合功能亦可得到<strong>一维差分电荷密度分布</strong>。步骤为先做差分电荷密度，然后命名为CHGCAR，再使用功能<code>316</code>做planar，其中一维电荷密度单位是e/A。</p><h4><a name="header-n198" class="md-header-anchor "/>3.6. 催化相关</h4><p><code>vaspkit 0.71</code>后增加了几个比较也特色的功能，其中几个是与催化相关。功能5中包含了几个已经开发的催化相关小工具。如下：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>9</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ==================== Catalysis-ElectroChem Kit ==================</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 501) Thermal Corrections for Adsorbate</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 502) Thermal Corrections for Gas</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 503) d-Band Center (experimental)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 504) Convert NEB-Path to PDB Format for Animation</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 505) Interpolate NEB Images Linearly</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 507) Imaginary Frequencies Correction</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 508) Bader2PQR (Shown in VMD by atomic charge)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 509) Evaluate half life period for a first order reaction                                                                                 </span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 200px;"/><div class="CodeMirror-gutters" style="height: 200px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>其中功能<code>501</code>和<code>502</code>已经介绍，<code>503</code>是用来计算催化剂d带中心。d带中心的相关知识可以查看研之成理何政达的文章<a href="https://www.wxwenku.com/d/102737820">d能带中心——最成功的描述符</a>。</p><h5><a name="header-n202" class="md-header-anchor "/>将NEB路径转成PDB文件以可视化</h5><p>功能<code>504</code>将<code>Nudged Elastic Band</code>（一种过渡态的搜索方法）的<code>images</code>组合成多帧PDB文件，通过可视化该文件可以查看<code>VTST</code>脚本插值生成的路径是不是我们<a href="http://blog.sina.com.cn/s/blog_b364ab230102vghk.html">预期的能量路径</a>。<code>VTST</code>的<code>nebmovie.pl</code>可以将<code>images</code>组合成多帧xyz结构文件，但是由于xyz文件不包含晶格信息，无法查看周期性的映像，若分子处于盒子边缘，可能无法查看完整的能量路径。以目录中的ORR反应（/examples/nudged_elastic_band/neb_animation）为例说明功能<code>504</code>的用法。启动<code>VASPKIT</code>,输入<code>5</code>选择功能<code>Catalysis-ElectroChem Kit</code>，在下一个界面输入<code>504</code>选择<code>TheConvert NEB-Path to PDB Format for Animation</code>。<code>VASPKIT</code>将会从00~07目录里面读取POSCAR组合生成<code>NEB_*.pdb</code>。</p><blockquote><p>提交任务前，我要检查一遍设想的对不对，运行一下504得到一个<code>NEB_initial.pdb</code>文件。提交任务后，比如说算了30步，我想查看一下算的怎么样了，需要再运行一下504，得到一个<code>NEB_30.pdb</code>文件,同时提示你<code>NEB is still runing, NOW 30 step!</code>。如果任务算完了，我运行下504,得到<code>NEB_final.pdb</code> 文件,同时提示你<code>NEB has finished</code>。 如果NSW设置的100，跑了100步没有收敛，运行504同样会得到得到<code>NEB_100_end.pdb</code>文件，但是会提示你<code>NEB has stopped, but has reached NSW step, NOT converged!</code>。`</p></blockquote><p>启动VMD，将<code>NEB.pdb</code>拖入VMD，切换显示方式，在VMD主窗口选择菜单<code>Display</code>,选择<code>Orthographic</code>正交显示模式。然后在VMD主窗口选择菜单<code>Graphics</code>，再选择<code>Representations</code>，<code>Drawing Methods</code>选择<code>CPK</code>。默认是不显示盒子边界的，在VMD主窗口选择菜单<code>Extensions</code>,选择<code>Tk Console</code>,在<code>VMD TkConsole</code>窗口中输入<code>pbc box -color white</code>，就可以显示完整的体系，如下</p><p><img src="vmd-1.jpg" alt="Alt text" referrerpolicy="no-referrer"/></p><p>如果分子处于边界，为了查看完整的振动，可以开启周期性。在<code>Representations</code>面板里选择<code>Periodic</code>，选择在x，y，z方向上是否显示周期性。</p><p><img src="vmd-2.jpg" alt="Alt text" referrerpolicy="no-referrer"/></p><p>主窗口的底栏可以为动画功能栏，点击最右下角的小箭头就可以播放多帧动画。通过查看振动方向，可以判断<code>nebmake.pl</code>线性插的点是否合理。</p><blockquote><p>李强提出可以实时通过显示每个Image中成键原子间的键长来判断插值的点是否合理。在VMD主窗口选择菜单 Mouse --> Label --> 2， 然后去模型界面上，点与NEB路径中最相关的2个原子，就可以查看NEB路径中，原子间距离随着IMAGE结构的变化了。 </p></blockquote><h5><a name="header-n213" class="md-header-anchor "/>线性插点生成NEB的路径</h5><p>功能 505 通过线性插点生成NEB所需的images，功能类似于<code>nebmake.pl</code> 。目录<code>/vaspkit.0.73/examples/nudged_elastic_band/neb_make</code>有ORR反应的测试例子。启动功能505后，接着输入 Initial_POSCAR，final_POSCAR和images数目。  </p><p>本例中输入<code>ini/POSCAR fin/POSCAR 3</code>，即可在初态和末态之间插3个images。再通过功能<code>504</code>将生成的路径转换成PDB，通过<code>VMD</code>等可视化软件可以观察到NEB的路径。</p><h5><a name="header-n216" class="md-header-anchor "/>虚频校正</h5><p>功能507 能够校正振动分析中不想要的小虚频。为了验证优化的结构是否处于势能面的极值点，我们就会进行频率分析（IBRION=5）。常会发现有很多波数非常小的虚频（几十cm-1），李强建议，一般小于50cm-1的虚频可以忽略，一般都是为了破坏对称性而产生的虚频，并不是我们想要的过渡态虚频。因此可以通过此功能消除。进行频率分析后，启动功能<code>507</code>，如果所有虚频的波数都小于50cm-1，自动校正所有的虚频振动，如果有1个大于50cm-1的虚频，此时可能会出现过渡态的虚频，会提示你是否保留最大的虚频。可以用<code>JMOL</code>等软件查看最大虚频所对应的振动是否是过渡态的虚频振动方向，如果是，选择<code>yes</code>保留。本例中选择<code>no</code>，校正所有虚频。接下来按照提示输入频率矫正因子0.1即可生成虚频校正后的结构文件<code>POSCAR_NEW</code>。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>4</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">The max imag_fre is  <span class="cm-number">477</span>.69 cm-1, whether to keep it? Type <span class="cm-builtin">yes</span> or no!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">no</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Please input the imaginary-freq correction factor, usually <span class="cm-number">0</span>.1 is enough!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">0</span>.1</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 80px;"/><div class="CodeMirror-gutters" style="height: 80px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p><code>/vaspkit.0.73/examples/thermo_correction/H2</code>目录下展示了H2分子的虚频校正。</p><p>未校正前的虚频有两个波数比较大的虚频：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>4</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-def">$ grep</span> f/i OUTCAR</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-number">4</span> f<span class="cm-def">/i</span><span class="cm-operator">=</span>   <span class="cm-number">0</span>.006948 THz   <span class="cm-number">0</span>.043656 2PiTHz  <span class="cm-number">0</span>.231765 cm-1    <span class="cm-number">0</span>.028735 meV</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-number">5</span> f<span class="cm-def">/i</span><span class="cm-operator">=</span>  <span class="cm-number">14</span>.187904 THz   <span class="cm-number">89</span>.145228 2PiTHz <span class="cm-number">473</span>.257512 cm-1  <span class="cm-number">58</span>.676474 meV</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-number">6</span> f<span class="cm-def">/i</span><span class="cm-operator">=</span>  <span class="cm-number">14</span>.320738 THz   <span class="cm-number">89</span>.979853 2PiTHz <span class="cm-number">477</span>.688402 cm-1  <span class="cm-number">59</span>.225835 meV</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 80px;"/><div class="CodeMirror-gutters" style="height: 80px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>校正后<strong>再优化一遍分子</strong>并进行频率分析。</p><blockquote><p>需要强调的是，虚频的校正是按照振动方向的位移乘以缩放系数叠加到原有的原子坐标上，<strong>纯属经验操作，没有理论依据</strong> 。优化和振动分析必须在相同级别才有意义。<code>sobereva</code>建议，振动分析后出现虚频，说明优化精度明显不够，可以提高收敛精度(降低<code>EDIFFG</code>并且<code>IBRION=1</code>)，也可以试试本工具。<strong>如果有多个虚频，一次通过微调结构消除所有虚频的可能性比较低</strong> 。如果体系比较大，虚频涉及的原子不在自己的兴趣当中，不消掉虚频也无大碍。</p></blockquote><h5><a name="header-n225" class="md-header-anchor "/>估算一级反应的反应速率和半衰期</h5><p>根据公式<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="19.062ex" height="3.715ex" viewbox="0 -1106.5 8207.1 1599.4" role="img" focusable="false" style="vertical-align: -1.145ex;"><defs><path stroke-width="0" id="E16-MJMATHI-6B" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 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transform="scale(0.707)" xlink:href="#E16-MJMAIN-394" x="778" y="0"/><g transform="translate(1139,0)"><use transform="scale(0.707)" xlink:href="#E16-MJMATHI-47" x="0" y="0"/><use transform="scale(0.5)" xlink:href="#E16-MJMAIN-2218" x="1111" y="610"/><g transform="translate(555,-175)"><use transform="scale(0.5)" xlink:href="#E16-MJMATHI-54" x="0" y="0"/><use transform="scale(0.5)" xlink:href="#E16-MJMATHI-53" x="704" y="0"/></g></g><use transform="scale(0.707)" xlink:href="#E16-MJMAIN-2F" x="3450" y="0"/><g transform="translate(2793,0)"><use transform="scale(0.707)" xlink:href="#E16-MJMATHI-6B" x="0" y="0"/><use transform="scale(0.5)" xlink:href="#E16-MJMATHI-42" x="736" y="-213"/></g><use transform="scale(0.707)" xlink:href="#E16-MJMATHI-54" x="5108" y="0"/></g></g></g></svg></span> 代入温度和自由能垒进行估算，一般认为反应能垒<code>21Kcal/mol</code>的反应在常温下容易发生。</p><p>启动<code>vaspkit</code>，输入功能<code>509</code>，进入功能<code>Evaluate half life period for a first order reaction</code>，输入温度<code>298.15K</code>，反应能垒<code>21Kcal/mol</code>，得到反应的半衰期为<code>0.077h</code>,也就是反应物消耗一半所需的时间。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>7</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">510</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Please Input temperature <span class="cm-keyword">in</span> K</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">298</span>.15</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Please Input energy barrier <span class="cm-keyword">in</span> Kcal/mol</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">21</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Rate constant is <span class="cm-number">0</span>.003 s-</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Half life period is <span class="cm-number">0</span>.077 h</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 140px;"/><div class="CodeMirror-gutters" style="height: 140px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p> </p><h5><a name="header-n230" class="md-header-anchor "/>结构操作小工具</h5><p>主功能4 <code>Structure Editor</code> 包含了几个结构操作的小工具。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>8</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> =================== Structure Operations ========================</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 400) Redefine Lattice (experimental)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 401) Build Supercell</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 402) Fix atoms (FFF) by Layers</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 403) Fix atoms (FFF) by Heights</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 404) Apply Random-Displacement on Atomic-Positions</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 405) Converte XDATCAR to PDB Format for Animation</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> 409) Remove Spurious Lattice-Distortion after Optimization</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 160px;"/><div class="CodeMirror-gutters" style="height: 160px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>功能<code>400</code>为测试功能，在寻找<code>primitive cell</code>之后，有些二维体系的真空层会变成<code>x</code>或<code>y</code>方向，可以使用此功能重新设置沿<code>z</code>方向。功能<code>401</code>用于结构扩胞，新版本进行了改进，在扩胞后能够保留原有结构中的<code>Selective Information</code>，也就是原子的位置限制信息。以纤锌矿<code>ZnO</code>的<code>0001</code>面结构为例。在优化过程中固定了底部的三层（<code>Zn-O</code>双层）和钝化氢，而放开表面的三层（<code>Zn-O</code>双层）弛豫模拟表面。扩胞时，在<code>x</code>,<code>y</code>方向上的同层原子的位置固定信息将会一致。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>22</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">ZnO-1811117\(0\0\1)                     </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   1.00000000000000     </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     3.2890999317000000    0.0000000000000000    0.0000000000000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    -1.6445499659000000    2.8484440965000002    0.0000000000000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     0.0000000000000000    0.0000000000000000   31.0000000000000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   O    Zn   H </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     6     6     1</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Selective dynamics</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Direct</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.6666700244773196  0.3333300053761477  0.1505069039677451   F   F   F</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.6666716924670117  0.3333278011868069  0.3220708624919105   T   T   T</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.6666726846730975  0.3333236596434402  0.4952603515620634   T   T   T</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.3333300053138402  0.6666700242891679  0.0649169839032240   F   F   F</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.3333300053138402  0.6666700242891679  0.2361085000000003   F   F   F</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.3333199694428693  0.6666773648761363  0.4080366153030212   T   T   T</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.6666700244773196  0.3333300053761477  0.0855899113548375   F   F   F</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.6666700244773196  0.3333300053761477  0.2567814361612903   F   F   F</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">18</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.6666745852439349  0.3333222632901633  0.4277261402910583   T   T   T</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">19</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.3333300053138402  0.6666700242891679  0.1711915073870998   F   F   F</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">20</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.3333495480118175  0.6666503610072737  0.3422927302063438   T   T   T</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">21</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.3333226658022473  0.6666735134936482  0.5114804524358304   T   T   T</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">22</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  0.3353480398005857  0.6659931540629387  0.0310253291612881   F   F   F</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 440px;"/><div class="CodeMirror-gutters" style="height: 440px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>功能<code>402</code>,<code>403</code>在表面模拟中非常有用。功能<code>402</code>会自动依据不同的阈值对原子的Z方向坐标进行分层，提示用户使用不同的阈值时体系在Z方向有几层原子，用户再根据自己的判断输入新的阈值重新进行原子分层，并输入需要固定的底部几层原子，得到底部固定，表面放开的结构文件。
同样以纤锌矿<code>ZnO</code>的<code>0001</code>面为例，我们想固定底部4层（<code>Zn-O</code>双层），只放开表面两层。启动<code>VASPKIT</code>,输入<code>4</code>选择功能<code>Structure Manipulator</code>，在下一个界面输入<code>402</code>选择<code>Fix atoms (FFF) by Layers</code>。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>11</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  Threshold:  0.3 layers:  13</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Threshold:  0.6 layers:  12</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Threshold:  0.9 layers:   7</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Threshold:  1.2 layers:   7</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Threshold:  1.5 layers:   7</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Please choose a threshold to separate layers-></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">1.5</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |               Selective Dynamics is Activated!                |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Found 7 layers, choose how many layers to be fixed</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 220px;"/><div class="CodeMirror-gutters" style="height: 220px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>我们判断CONTCAR在Z方向有7层原子，所以我们选择阈值1.5<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.583ex" height="2.575ex" viewbox="0 -799.7 681.7 1108.5" role="img" focusable="false" style="vertical-align: -0.717ex;"><defs/><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><text font-family="STIXGeneral,'Arial Unicode MS',serif" stroke="none" transform="scale(61.362) matrix(1 0 0 -1 0 0)">Å</text></g></svg></span> 进行分层，并选择固定底部5层（包含最后一层钝化氢），就会生成<code>CONTCAR_fix</code>。程序在固定完原子后会输出哪些原子被固定住了，帮助我们确认固定是否正确。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>13</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     1.6445664829999989     0.9494718860000013     4.6657140230000982  F F F </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     1.6445755940842863     0.9494656074898858     9.9841967372492260  F F F </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     1.6445856685242579     0.9494538105351326    15.3530708984239652  T T T </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    -0.0000164679999908     1.8989722949999921     2.0124265009999438  F F F </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    -0.0000164679999908     1.8989722949999921     7.3193635000000095  F F F </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    -0.0000615489445641     1.8989932042516069    12.6491350743936568  T T T </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     1.6445664829999989     0.9494718860000013     2.6532872519999624  F F F </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     1.6445664829999989     0.9494718860000013     7.9602245209999989  F F F </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     1.6445942160644029     0.9494498331008844    13.2595103490228077  T T T </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    -0.0000164679999908     1.8989722949999921     5.3069367290000935  F F F </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     0.0000801471361600     1.8989162852407626    10.6110746363966584  F F F </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    -0.0000463465581788     1.8989822338038955    15.8558940255107430  T T T </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     0.0077341959999959     1.8970442679999928     0.9617852039999312  F F F </span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 260px;"/><div class="CodeMirror-gutters" style="height: 260px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>有时候对于复杂的体系，很难通过选择层达到我们的目的，在刘锦程的建议下，开发了功能<code>403</code>，通过选择高度区间固定原子。通过在其他可视化软件中确定需要固定的原子层所处的高度区间，在<code>VASPKIT</code>中选择高度区间固定原子。<code>vaspkit.0.73/utilities/</code>目录下有该功能的扩展脚本<code>POSCARtoolkit</code>，可以实现对部分原子固定或弛豫的功能。</p><p>当然我们可以手动在<code>Material Studio</code>中<strong>可视化地固定原子</strong>，导出<code>xsd</code>后使用功能<code>106</code>将含有位置限制信息的<code>xsd</code>转换成<code>POSCAR</code>。</p><p>功能<code>405</code>,<code>Converte XDATCAR to PDB for Animation</code>与功能<code>504</code>相似，能够将分子动力学、普通优化，<code>晶格优化过程</code>中<code>XDATCAR</code>记录的离子步转化成可以可视化的多帧PDB文件。VMD，OVITO等可视化软件只能可视化分子动力学、普通优化的离子步，对于晶格优化（<code>ISIF=3</code>）的XDATCAR只能查看第一帧结构。而<code>VASPKIT</code>生成的<code>XDATCAR.pdb</code>同样可以由VMD查看离子步的优化过程。</p><h4><a name="header-n242" class="md-header-anchor "/>3.7.  能带反折叠计算 </h4><p>能带折叠的主要作用是因为合金需要使用超胞计算，为了和单胞的能带对比需要把超胞的能带折叠成 effective band structure (EBS)。</p><p>以石墨烯为例（详见<code>vaspkit.0.73/examples/band_unfolding/graphene_2x2</code>）。</p><p>第一步，准备POSCAR；</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>11</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Graphene                             </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-number">1</span>.00000000000000     </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     <span class="cm-number">1</span>.2344083195740001   <span class="cm-attribute">-2</span>.1380573715510001    <span class="cm-number">0</span>.0000000000000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     <span class="cm-number">1</span>.2344083195740001    <span class="cm-number">2</span>.1380573715510001    <span class="cm-number">0</span>.0000000000000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     <span class="cm-number">0</span>.0000000000000000    <span class="cm-number">0</span>.0000000000000000   <span class="cm-number">12</span>.0000000000000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   C </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">     <span class="cm-number">2</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Direct</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  <span class="cm-number">0</span>.0000000000000000  <span class="cm-number">0</span>.0000000000000000  <span class="cm-number">0</span>.5000000000000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  <span class="cm-number">0</span>.3333329999917112  <span class="cm-number">0</span>.6666670000099160  <span class="cm-number">0</span>.5000000000000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 220px;"/><div class="CodeMirror-gutters" style="height: 220px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>第二步：准备<code>KPATH.in</code>文件，对于二维体系，可通过<code>vaspkit</code> <code>302</code>命令产生推荐能带路径；</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>13</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Generated by VASPKIT.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-number">30</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Line-Mode</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Reciprocal</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-number">0</span>.0000000000   <span class="cm-number">0</span>.0000000000   <span class="cm-number">0</span>.0000000000     GAMMA          </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-number">0</span>.5000000000   <span class="cm-number">0</span>.0000000000   <span class="cm-number">0</span>.0000000000     M              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-number">0</span>.5000000000   <span class="cm-number">0</span>.0000000000   <span class="cm-number">0</span>.0000000000     M              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-number">0</span>.3333333333   <span class="cm-number">0</span>.3333333333   <span class="cm-number">0</span>.0000000000     K              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-number">0</span>.3333333333   <span class="cm-number">0</span>.3333333333   <span class="cm-number">0</span>.0000000000     K              </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   <span class="cm-number">0</span>.0000000000   <span class="cm-number">0</span>.0000000000   <span class="cm-number">0</span>.0000000000     GAMMA          </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 260px;"/><div class="CodeMirror-gutters" style="height: 260px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>第三步：利用 <code>vaspkit</code> <code>401</code>命令建立2x2超胞，然后<code>mv SC221.vasp POSCAR</code>，并新建<code>KPKIT.in</code>文件，并在第一行输入超胞大小<code>2 2 1</code>；</p><p>第四步：运行<code>vaspkit</code> <code>281</code>命令，生成用于超胞计算KPOINTS文件；运行VASP。</p><p>第五步：运行<code>vaspkit</code> <code>282</code>命令，提取包含有效能带（Effective Band Structure）数据<code>EBS.dat</code>文件；</p><p>第六步：<code>python ebs.py</code>画图；</p> <div align="center"><img src="./ebs.jpg" width="50%" height="50%" onerror="this.style.display = 'none';"/></div>   <h4><a name="header-n254" class="md-header-anchor "/>3.8 3D能带计算</h4><p>二维材料3D能带计算，这里以石墨烯为例，见<code>vaspkit.0.73/examples/3D_band</code>。</p><p>第一步，准备好石墨烯的POSCAR和用于静态计算的INCAR文件；</p><p>第二步：运行<code>VASPKIT</code>并选择<code>231</code>生成用于<strong>3D能带计算</strong> 的KPOINTS文件，执行界面如下所示。<strong>注意为了获得平滑的3D能带面，用于产生KPOINTS文件的分辨率值应该设置在0.001左右</strong> ；</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>13</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-attribute">------------</span>>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">231</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-operator">+</span><span class="cm-attribute">--------------------------</span> Warm Tips <span class="cm-attribute">--------------------------</span><span class="cm-operator">+</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   \* Accuracy Levels: (1) Low:    <span class="cm-number">0</span>.04~0.03;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                      (2) Medium: <span class="cm-number">0</span>.03~0.02;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                      (3) Fine:   <span class="cm-number">0</span>.02~0.01.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   \* <span class="cm-number">0</span>.015 is Generally Precise Enough!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-operator">+</span><span class="cm-attribute">---------------------------------------------------------------</span><span class="cm-operator">+</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Input KP-Resolved Value (unit: <span class="cm-number">2</span>*PI/Ang):</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">------------</span>>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">0</span>.008</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (1) Reading Structural Parameters from POSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (2) Written KPOINTS File!</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 260px;"/><div class="CodeMirror-gutters" style="height: 260px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>第三步，提交VASP作业；</p><p>第四步，待VASP计算完成后，再次运行<code>VASPKIT</code>，输入<code>232</code>或<code>233</code>命令。<code>233</code>命令可一次性输入包含价带顶的<code>BAND.HOMO.grd</code>和导带底的<code>BAND.LUMO.grd</code>文件的能带；<code>232</code>可以得到其它任意能带的计算数据，这里我们选择<code>233</code>，执行界面如下所示。</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>14</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-attribute">------------</span>>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">233</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-operator">+</span><span class="cm-attribute">--------------------------</span> Warm Tips <span class="cm-attribute">--------------------------</span><span class="cm-operator">+</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">           ONLY Reliable <span class="cm-keyword">for</span> Band-Structure Calculations!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-operator">+</span><span class="cm-attribute">---------------------------------------------------------------</span><span class="cm-operator">+</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (1) Reading Input Parameters From INCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (2) Reading Structural Parameters from POSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (3) Reading Fermi-Level From DOSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">ooooooooo The Fermi Energy will be <span class="cm-keyword">set</span> to zero eV oooooooooooooooo</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (4) Reading Energy-Levels From EIGENVAL File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (5) Reading Kmesh From KPOINTS File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (6) Written BAND.HOMO.grd File.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (7) Written BAND.LUMO.grd File.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (8) Written KX.grd and KY.grd Files.</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 280px;"/><div class="CodeMirror-gutters" style="height: 280px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>第五步：运行<code>python how_to_visual.py</code>，绘制3D能带图(python2.7环境)。</p><p> <img src="3D.png" alt="img" referrerpolicy="no-referrer"/> </p><h4><a name="header-n264" class="md-header-anchor "/>3.9 费米面计算</h4><p>费米面计算，这里我们以Cu为例，见<code>vaspkit.0.73/examples/Cu_fermi_surface</code>。</p><p>第一步，准备好<code>FCC Cu</code>的POSCAR，注意一定是原胞（<strong>primitive cell</strong> ）和用于静态计算的INCAR文件；</p><p>第二步，运行<code>VASPKIT</code>，输入<code>261</code>命令，产生用于计算计算费米面的<code>KPOINTS</code>和<code>POTCAR</code>文件，执行界面如下图所示；</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>12</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-attribute">------------</span>>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">261</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-operator">+</span><span class="cm-attribute">--------------------------</span> Warm Tips <span class="cm-attribute">--------------------------</span><span class="cm-operator">+</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   \* Accuracy Levels: (1) Medium: <span class="cm-number">0</span>.02~0.01;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                      (2) Fine:      < <span class="cm-number">0</span>.01;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   \* <span class="cm-number">0</span>.01 is Generally Precise Enough!</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-operator">+</span><span class="cm-attribute">---------------------------------------------------------------</span><span class="cm-operator">+</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Input KPT-Resolved Value (unit: <span class="cm-number">2</span>*PI/Angstrom):</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">------------</span>>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">0</span>.008</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (1) Reading Structural Parameters from POSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (2) Written KPOINTS File!</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 240px;"/><div class="CodeMirror-gutters" style="height: 240px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>第三步，提交VASP作业；</p><p>第四步，待VASP计算完成后，再次运行<code>VASPKIT</code>，输入<code>262</code>命令，生成包含费米面数据的<code>FERMISURFACE.bxsf</code>文件，执行界面如下图所示；</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>8</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-attribute">------------</span>>></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">262</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (1) Reading Input Parameters From INCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (2) Reading Structural Parameters from POSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (3) Reading Fermi-Level From DOSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">ooooooooo The Fermi Energy will be <span class="cm-keyword">set</span> to zero eV oooooooooooooooo</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (4) Reading Energy-Levels From EIGENVAL File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-attribute">--</span>>> (5) Written FERMISURFACE.bxsf File!</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 160px;"/><div class="CodeMirror-gutters" style="height: 160px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>第五步，运行<code>XcrySDen</code>软件，按照下图步骤。我们发现第五条能带穿过费米面，因此我们选择<code>Band Number 5</code>，然后点击<code>Selected</code>，然后得到Cu的费米面。</p> <div align="center"><img src="fermi1.jpg" width="70%" height="70%" onerror="this.style.display = 'none';"/></div> 
 <div align="center"><img src="fermi2.jpg" width="70%" height="70%" onerror="this.style.display = 'none';"/></div><h4><a name="header-n275" class="md-header-anchor "/>3.10 VASP2BoltzTraP接口</h4><p>该功能介绍由<code>王宁_电子科大_二维材料</code>贡献。<code>VASP+BoltzTraP</code>能够计算材料的热电性质，其计算流程为：先使用VASP进行DFT计算，得到材料的电子结构，再利用<code>BoltzTraP</code>计算其输运性质。在两个软件之间，需要一个转化接口，以实现将VASP的输出文件转化为<code>BoltzTraP</code>的输入文件。<code>BoltzTraP</code>手册给出了一种转化方法：利用<code>ase库</code>、<code>vasp2boltz.py</code> 和<code>vasp2boltz.txt</code>文件实现，但是操作十分繁琐。利用<code>vaspkit</code>中的<code>VASP2BoltzTraP Interface</code>，能够一键实现VASP与<code>BoltzTraP</code>之间的文件转化。</p><p>具体使用方法如下：</p><ol start=""><li>利用VASP进行结构优化。</li><li>采用高密度的KPOINTS（MP sampling）进行自洽计算。这个高密度是在你的计算资源允许的前提下，尽可能的高。</li><li>将第2步计算得到的<code>OUTCAR POSCAR EIGENVAL DOSCAR</code>文件拷贝到新建文件夹下，并将此文件夹命名为case。（PS：省事的做法是将自洽的文件夹拷贝一份直接命名为case）。</li><li>在case文件夹下，输入<code>vaspkit</code>呼出菜单，选择<code>VASP2BoltzTraP Interface</code>选项，得到<code>BoltzTraP</code>所需的三个输入文件<code>case.intrans, case.struct, case.energy</code>，修 改 <code>case.struct</code> 和<code>case.energy</code> 中第一行名称为 case。</li><li>运行 <code>~/src/x_trans BoltzTraP</code></li></ol><h4><a name="header-n289" class="md-header-anchor "/>3.11 基于能量-应变关系计算弹性常数</h4><p>      在材料的线性形变范围内（应变较小的情况下），体系的应力与应变满足胡克定律，</p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n291" cid="n291" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-3-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="94.3229px" height="53.0903px" viewbox="0 -1842.8 5784.8 3256.2" role="img" focusable="false" style="vertical-align: -3.283ex; max-width: 100%;"><defs><path stroke-width="0" id="E3-MJMATHI-3C3" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 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xlink:href="#E3-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E3-MJMATHI-6A" x="659" y="-213"/></g></g></svg></span></div></div></div><p>       其中<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.125ex" height="1.858ex" viewbox="0 -552.9 915 799.8" role="img" focusable="false" style="vertical-align: -0.573ex;"><defs><path stroke-width="0" id="E28-MJMATHI-3C3" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z"/><path stroke-width="0" id="E28-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E28-MJMATHI-3C3" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E28-MJMATHI-69" x="807" y="-213"/></g></svg></span> 和<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.028ex" height="1.862ex" viewbox="0 -554.3 873 801.7" role="img" focusable="false" style="vertical-align: -0.575ex;"><defs><path stroke-width="0" id="E23-MJMATHBI-3B5" d="M224 -17Q126 -17 81 22T36 112Q36 178 84 226L93 236L88 246Q79 264 79 289Q79 341 124 388Q201 461 333 461Q402 461 455 425Q480 409 481 390Q481 365 464 350T428 334Q415 334 387 352T313 370Q141 370 141 293Q141 275 146 270Q147 270 148 270T155 272Q202 291 263 291H270Q349 291 349 244Q349 195 281 183Q274 182 239 182Q201 182 184 185T137 200Q123 188 112 168T100 129T112 98T148 81T189 75T237 74H243H251Q288 74 310 75T359 86T398 112Q405 124 417 124Q426 124 432 117T439 100Q439 88 427 70T390 32T322 -3T224 -17ZM286 238Q286 240 253 240Q245 240 234 239T216 237T209 235Q209 232 250 232Q286 232 286 238Z"/><path stroke-width="0" id="E23-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E23-MJMATHBI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E23-MJMATHI-69" x="748" y="-213"/></g></svg></span> 分别表示应力和应变，<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.136ex" height="2.717ex" viewbox="0 -799.7 1350.3 1169.9" role="img" focusable="false" style="vertical-align: -0.86ex;"><defs><path stroke-width="0" id="E20-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"/><path stroke-width="0" id="E20-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"/><path stroke-width="0" id="E20-MJMATHI-6A" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E20-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E20-MJMATHI-69" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E20-MJMATHI-6A" x="345" y="0"/></g></g></svg></span> 是弹性刚度常数，这里<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.318ex" height="2.29ex" viewbox="0 -738.3 4012.1 985.8" role="img" focusable="false" style="vertical-align: -0.575ex;"><defs><path stroke-width="0" id="E21-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"/><path stroke-width="0" id="E21-MJMAIN-2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"/><path stroke-width="0" id="E21-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"/><path stroke-width="0" id="E21-MJMAIN-36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E21-MJMAIN-31" x="0" y="0"/><use xlink:href="#E21-MJMAIN-2264" x="777" y="0"/><use xlink:href="#E21-MJMATHI-69" x="1833" y="0"/><use xlink:href="#E21-MJMAIN-2264" x="2456" y="0"/><use xlink:href="#E21-MJMAIN-36" x="3512" y="0"/></g></svg></span> ，即应变和应力分别有6个独立分量。</p><p>       施加应变后体系的应变能<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.926ex" height="2.86ex" viewbox="0 -861.1 5565.3 1231.2" role="img" focusable="false" style="vertical-align: -0.86ex;"><defs><path stroke-width="0" id="E22-MJMAIN-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"/><path stroke-width="0" id="E22-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"/><path stroke-width="0" id="E22-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"/><path stroke-width="0" id="E22-MJMATHI-56" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"/><path stroke-width="0" id="E22-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"/><path stroke-width="0" id="E22-MJMAIN-7B" d="M434 -231Q434 -244 428 -250H410Q281 -250 230 -184Q225 -177 222 -172T217 -161T213 -148T211 -133T210 -111T209 -84T209 -47T209 0Q209 21 209 53Q208 142 204 153Q203 154 203 155Q189 191 153 211T82 231Q71 231 68 234T65 250T68 266T82 269Q116 269 152 289T203 345Q208 356 208 377T209 529V579Q209 634 215 656T244 698Q270 724 324 740Q361 748 377 749Q379 749 390 749T408 750H428Q434 744 434 732Q434 719 431 716Q429 713 415 713Q362 710 332 689T296 647Q291 634 291 499V417Q291 370 288 353T271 314Q240 271 184 255L170 250L184 245Q202 239 220 230T262 196T290 137Q291 131 291 1Q291 -134 296 -147Q306 -174 339 -192T415 -213Q429 -213 431 -216Q434 -219 434 -231Z"/><path stroke-width="0" id="E22-MJMATHI-3B5" d="M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z"/><path stroke-width="0" id="E22-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"/><path stroke-width="0" id="E22-MJMAIN-7D" d="M65 731Q65 745 68 747T88 750Q171 750 216 725T279 670Q288 649 289 635T291 501Q292 362 293 357Q306 312 345 291T417 269Q428 269 431 266T434 250T431 234T417 231Q380 231 345 210T298 157Q293 143 292 121T291 -28V-79Q291 -134 285 -156T256 -198Q202 -250 89 -250Q71 -250 68 -247T65 -230Q65 -224 65 -223T66 -218T69 -214T77 -213Q91 -213 108 -210T146 -200T183 -177T207 -139Q208 -134 209 3L210 139Q223 196 280 230Q315 247 330 250Q305 257 280 270Q225 304 212 352L210 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xlink:href="#E22-MJMAIN-7D" x="1309" y="0"/></g><use xlink:href="#E22-MJMAIN-29" x="3412" y="0"/></g></g></svg></span> 可按应变张量<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.028ex" height="1.862ex" viewbox="0 -554.3 873 801.7" role="img" focusable="false" style="vertical-align: -0.575ex;"><defs><path stroke-width="0" id="E23-MJMATHBI-3B5" d="M224 -17Q126 -17 81 22T36 112Q36 178 84 226L93 236L88 246Q79 264 79 289Q79 341 124 388Q201 461 333 461Q402 461 455 425Q480 409 481 390Q481 365 464 350T428 334Q415 334 387 352T313 370Q141 370 141 293Q141 275 146 270Q147 270 148 270T155 272Q202 291 263 291H270Q349 291 349 244Q349 195 281 183Q274 182 239 182Q201 182 184 185T137 200Q123 188 112 168T100 129T112 98T148 81T189 75T237 74H243H251Q288 74 310 75T359 86T398 112Q405 124 417 124Q426 124 432 117T439 100Q439 88 427 70T390 32T322 -3T224 -17ZM286 238Q286 240 253 240Q245 240 234 239T216 237T209 235Q209 232 250 232Q286 232 286 238Z"/><path stroke-width="0" id="E23-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E23-MJMATHBI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E23-MJMATHI-69" x="748" y="-213"/></g></svg></span> 进行泰勒级数展开并取二阶近似得到：</p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n294" cid="n294" 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24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"/><path stroke-width="0" id="E27-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"/><path stroke-width="0" id="E27-MJMATHI-6A" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E27-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E27-MJMATHI-69" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E27-MJMATHI-6A" x="345" y="0"/></g></g></svg></span> 。第二种方法是能量-应变方法，即通过给结构施加不同应变后计算出体系总能相对于基态能量变化（应变能），再利用公式（2）进行二次多项式拟合，其中二次多项式系数是晶体的某个弹性常数或者弹性常数组合。第一种方法优点是每进行一次计算可一次得到<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.125ex" height="1.858ex" viewbox="0 -552.9 915 799.8" role="img" focusable="false" style="vertical-align: -0.573ex;"><defs><path stroke-width="0" id="E28-MJMATHI-3C3" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z"/><path stroke-width="0" id="E28-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E28-MJMATHI-3C3" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E28-MJMATHI-69" x="807" y="-213"/></g></svg></span> 六个独立分量，缺点是为了得到准确的应力大小，必须选择更高的截断能和更密集的K格点。在同样的精度下，能量-应变法相比应力-应变方法要求的截断能和K点数目相对较少，缺点是计算应变数目有所增加。VASPKIT中弹性常数计算基于能量-应变法。</p><p>这里我们以金刚石结构为例讲解如何采用能量-应变函数关系计算弹性常数，详见vaspkit/examples/elastic/diamond_3D。对于金刚石立方结构，一共有3个独立弹性常数，<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="8.136ex" height="2.575ex" viewbox="0 -799.7 3502.9 1108.5" role="img" focusable="false" style="vertical-align: -0.717ex;"><defs><path stroke-width="0" id="E29-MJMAIN-43" d="M56 342Q56 428 89 500T174 615T283 681T391 705Q394 705 400 705T408 704Q499 704 569 636L582 624L612 663Q639 700 643 704Q644 704 647 704T653 705H657Q660 705 666 699V419L660 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178T316 232Q316 267 309 298T295 344T269 400L259 396Q215 381 183 342T137 256T118 179T112 130Z"/><path stroke-width="0" id="E31-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E31-MJMATHI-3B5" x="0" y="0"/><use xlink:href="#E31-MJMAIN-3D" x="743" y="0"/><use xlink:href="#E31-MJMAIN-28" x="1799" y="0"/><use xlink:href="#E31-MJMAIN-30" x="2188" y="0"/><use xlink:href="#E31-MJMAIN-2C" x="2688" y="0"/><use xlink:href="#E31-MJMAIN-30" x="3133" y="0"/><use xlink:href="#E31-MJMAIN-2C" x="3633" y="0"/><use xlink:href="#E31-MJMAIN-30" x="4077" y="0"/><use xlink:href="#E31-MJMAIN-2C" x="4577" y="0"/><use xlink:href="#E31-MJMATHI-3B4" x="5022" y="0"/><use xlink:href="#E31-MJMAIN-2C" x="5473" y="0"/><use xlink:href="#E31-MJMATHI-3B4" x="5918" y="0"/><use xlink:href="#E31-MJMAIN-2C" x="6369" y="0"/><use xlink:href="#E31-MJMATHI-3B4" x="6813" y="0"/><use xlink:href="#E31-MJMAIN-29" x="7264" y="0"/></g></svg></span> ，可得<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="40.251ex" height="3.706ex" viewbox="0 -1103.9 17330 1595.6" role="img" focusable="false" style="vertical-align: -1.142ex;"><defs><path stroke-width="0" id="E32-MJMAIN-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"/><path stroke-width="0" id="E32-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"/><path stroke-width="0" id="E32-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"/><path stroke-width="0" id="E32-MJMATHI-56" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"/><path stroke-width="0" id="E32-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"/><path stroke-width="0" id="E32-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"/><path stroke-width="0" id="E32-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"/><path stroke-width="0" id="E32-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"/><path stroke-width="0" id="E32-MJMAIN-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"/><path stroke-width="0" id="E32-MJMATHI-3B5" d="M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z"/><path stroke-width="0" id="E32-MJMAIN-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"/><path stroke-width="0" id="E32-MJMAIN-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"/><path stroke-width="0" id="E32-MJMAIN-36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z"/><path stroke-width="0" id="E32-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E32-MJMAIN-394" x="0" y="0"/><use xlink:href="#E32-MJMATHI-45" x="833" y="0"/><use xlink:href="#E32-MJMAIN-3D" x="1874" y="0"/><g transform="translate(2652,0)"><g transform="translate(397,0)"><rect stroke="none" width="852" height="60" x="0" y="220"/><g transform="translate(60,541)"><use transform="scale(0.707)" xlink:href="#E32-MJMATHI-56" x="0" y="0"/><use transform="scale(0.5)" xlink:href="#E32-MJMAIN-30" x="824" y="-213"/></g><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-32" x="353" y="-560"/></g></g><g transform="translate(4023,0)"><use xlink:href="#E32-MJMAIN-28" x="0" y="0"/><g transform="translate(389,0)"><use xlink:href="#E32-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-34"/><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-34" x="500" y="0"/></g></g><g transform="translate(1911,0)"><use xlink:href="#E32-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-34" x="659" y="-213"/></g><g transform="translate(2830,0)"><use xlink:href="#E32-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-34" x="659" y="-213"/></g><use xlink:href="#E32-MJMAIN-2B" x="3972" y="0"/><g transform="translate(4972,0)"><use xlink:href="#E32-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-34"/><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-34" x="500" y="0"/></g></g><g transform="translate(6494,0)"><use xlink:href="#E32-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-35" x="659" y="-213"/></g><g transform="translate(7414,0)"><use xlink:href="#E32-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-35" x="659" y="-213"/></g><use xlink:href="#E32-MJMAIN-2B" x="8556" y="0"/><g transform="translate(9556,0)"><use xlink:href="#E32-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-34"/><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-34" x="500" y="0"/></g></g><g transform="translate(11078,0)"><use xlink:href="#E32-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-36" x="659" y="-213"/></g><g transform="translate(11997,0)"><use xlink:href="#E32-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E32-MJMAIN-36" x="659" y="-213"/></g><use xlink:href="#E32-MJMAIN-29" x="12917" y="0"/></g></g></svg></span> ，因此有<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="13.855ex" height="3.848ex" viewbox="0 -1042.7 5965.2 1656.8" role="img" focusable="false" style="vertical-align: -1.426ex;"><defs><path stroke-width="0" id="E33-MJMAIN-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"/><path stroke-width="0" id="E33-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"/><path stroke-width="0" id="E33-MJMATHI-56" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 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100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"/><path stroke-width="0" id="E33-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"/><path stroke-width="0" id="E33-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"/><path stroke-width="0" id="E33-MJMAIN-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"/><path stroke-width="0" id="E33-MJMATHI-3B4" d="M195 609Q195 656 227 686T302 717Q319 716 351 709T407 697T433 690Q451 682 451 662Q451 644 438 628T403 612Q382 612 348 641T288 671T249 657T235 628Q235 584 334 463Q401 379 401 292Q401 169 340 80T205 -10H198Q127 -10 83 36T36 153Q36 286 151 382Q191 413 252 434Q252 435 245 449T230 481T214 521T201 566T195 609ZM112 130Q112 83 136 55T204 27Q233 27 256 51T291 111T309 178T316 232Q316 267 309 298T295 344T269 400L259 396Q215 381 183 342T137 256T118 179T112 130Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1249" height="60" x="0" y="220"/><g transform="translate(60,424)"><use transform="scale(0.707)" xlink:href="#E33-MJMAIN-394" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E33-MJMATHI-45" x="833" y="0"/></g><g transform="translate(258,-408)"><use transform="scale(0.707)" xlink:href="#E33-MJMATHI-56" x="0" y="0"/><use transform="scale(0.5)" xlink:href="#E33-MJMAIN-30" x="824" y="-213"/></g></g><use xlink:href="#E33-MJMAIN-3D" x="1767" y="0"/><g transform="translate(2545,0)"><g transform="translate(397,0)"><rect stroke="none" width="473" height="60" x="0" y="220"/><use transform="scale(0.707)" xlink:href="#E33-MJMAIN-33" x="84" y="622"/><use transform="scale(0.707)" xlink:href="#E33-MJMAIN-32" x="84" y="-560"/></g></g><g transform="translate(3536,0)"><use xlink:href="#E33-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E33-MJMAIN-34"/><use transform="scale(0.707)" xlink:href="#E33-MJMAIN-34" x="500" y="0"/></g></g><g transform="translate(5058,0)"><use xlink:href="#E33-MJMATHI-3B4" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E33-MJMAIN-32" x="640" y="513"/></g></g></svg></span>  [1]。</p><p>设定<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="17.891ex" height="2.86ex" viewbox="0 -861.1 7702.9 1231.2" role="img" focusable="false" style="vertical-align: -0.86ex;"><defs><path stroke-width="0" id="E34-MJMATHI-3B5" d="M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z"/><path stroke-width="0" id="E34-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"/><path stroke-width="0" id="E34-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"/><path stroke-width="0" id="E34-MJMATHI-3B4" d="M195 609Q195 656 227 686T302 717Q319 716 351 709T407 697T433 690Q451 682 451 662Q451 644 438 628T403 612Q382 612 348 641T288 671T249 657T235 628Q235 584 334 463Q401 379 401 292Q401 169 340 80T205 -10H198Q127 -10 83 36T36 153Q36 286 151 382Q191 413 252 434Q252 435 245 449T230 481T214 521T201 566T195 609ZM112 130Q112 83 136 55T204 27Q233 27 256 51T291 111T309 178T316 232Q316 267 309 298T295 344T269 400L259 396Q215 381 183 342T137 256T118 179T112 130Z"/><path stroke-width="0" id="E34-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"/><path stroke-width="0" id="E34-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"/><path stroke-width="0" id="E34-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E34-MJMATHI-3B5" x="0" y="0"/><use xlink:href="#E34-MJMAIN-3D" x="743" y="0"/><use xlink:href="#E34-MJMAIN-28" x="1799" y="0"/><use xlink:href="#E34-MJMATHI-3B4" x="2188" y="0"/><use xlink:href="#E34-MJMAIN-2C" x="2639" y="0"/><use xlink:href="#E34-MJMATHI-3B4" x="3084" y="0"/><use xlink:href="#E34-MJMAIN-2C" x="3535" y="0"/><use xlink:href="#E34-MJMAIN-30" x="3979" y="0"/><use xlink:href="#E34-MJMAIN-2C" x="4479" y="0"/><use xlink:href="#E34-MJMAIN-30" x="4924" y="0"/><use xlink:href="#E34-MJMAIN-2C" x="5424" y="0"/><use xlink:href="#E34-MJMAIN-30" x="5869" y="0"/><use xlink:href="#E34-MJMAIN-2C" x="6369" y="0"/><use xlink:href="#E34-MJMAIN-30" x="6813" y="0"/><use xlink:href="#E34-MJMAIN-29" x="7313" y="0"/></g></svg></span> ，可得<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="50.457ex" height="3.564ex" viewbox="0 -1042.7 21724.5 1534.4" role="img" focusable="false" style="vertical-align: -1.142ex;"><defs><path stroke-width="0" id="E35-MJMAIN-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"/><path stroke-width="0" id="E35-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"/><path stroke-width="0" id="E35-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"/><path stroke-width="0" id="E35-MJMATHI-56" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"/><path stroke-width="0" id="E35-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"/><path stroke-width="0" id="E35-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"/><path stroke-width="0" id="E35-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"/><path stroke-width="0" id="E35-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"/><path stroke-width="0" id="E35-MJMATHI-3B5" d="M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z"/><path stroke-width="0" id="E35-MJMAIN-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"/><path stroke-width="0" id="E35-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E35-MJMAIN-394" x="0" y="0"/><use xlink:href="#E35-MJMATHI-45" x="833" y="0"/><use xlink:href="#E35-MJMAIN-3D" x="1874" y="0"/><g transform="translate(2652,0)"><g transform="translate(397,0)"><rect stroke="none" width="663" height="60" x="0" y="220"/><use transform="scale(0.707)" xlink:href="#E35-MJMATHI-56" x="84" y="622"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-32" x="219" y="-560"/></g></g><g transform="translate(3834,0)"><use xlink:href="#E35-MJMAIN-28" x="0" y="0"/><g transform="translate(389,0)"><use xlink:href="#E35-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-31"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-31" x="500" y="0"/></g></g><g transform="translate(1911,0)"><use xlink:href="#E35-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-31" x="659" y="-213"/></g><g transform="translate(2830,0)"><use xlink:href="#E35-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-31" x="659" y="-213"/></g><use xlink:href="#E35-MJMAIN-2B" x="3972" y="0"/><g transform="translate(4972,0)"><use xlink:href="#E35-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-31"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-31" x="500" y="0"/></g></g><g transform="translate(6494,0)"><use xlink:href="#E35-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-32" x="659" y="-213"/></g><g transform="translate(7414,0)"><use xlink:href="#E35-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-32" x="659" y="-213"/></g><use xlink:href="#E35-MJMAIN-2B" x="8556" y="0"/><g transform="translate(9556,0)"><use xlink:href="#E35-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-31"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-32" x="500" y="0"/></g></g><g transform="translate(11078,0)"><use xlink:href="#E35-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-31" x="659" y="-213"/></g><g transform="translate(11997,0)"><use xlink:href="#E35-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-32" x="659" y="-213"/></g><use xlink:href="#E35-MJMAIN-2B" x="13139" y="0"/><g transform="translate(14139,0)"><use xlink:href="#E35-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-31"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-32" x="500" y="0"/></g></g><g transform="translate(15662,0)"><use xlink:href="#E35-MJMATHI-3B5" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E35-MJMAIN-32" x="659" y="-213"/></g><g 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0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"/><path stroke-width="0" id="E36-MJMATHI-56" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"/><path stroke-width="0" id="E36-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"/><path stroke-width="0" id="E36-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"/><path stroke-width="0" id="E36-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 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686T302 717Q319 716 351 709T407 697T433 690Q451 682 451 662Q451 644 438 628T403 612Q382 612 348 641T288 671T249 657T235 628Q235 584 334 463Q401 379 401 292Q401 169 340 80T205 -10H198Q127 -10 83 36T36 153Q36 286 151 382Q191 413 252 434Q252 435 245 449T230 481T214 521T201 566T195 609ZM112 130Q112 83 136 55T204 27Q233 27 256 51T291 111T309 178T316 232Q316 267 309 298T295 344T269 400L259 396Q215 381 183 342T137 256T118 179T112 130Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1249" height="60" x="0" y="220"/><g transform="translate(60,425)"><use transform="scale(0.707)" xlink:href="#E36-MJMAIN-394" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E36-MJMATHI-45" x="833" y="0"/></g><g transform="translate(258,-409)"><use transform="scale(0.707)" xlink:href="#E36-MJMATHI-56" x="0" y="0"/><use transform="scale(0.5)" xlink:href="#E36-MJMAIN-30" x="824" y="-213"/></g></g><use xlink:href="#E36-MJMAIN-3D" x="1767" y="0"/><g transform="translate(2822,0)"><use xlink:href="#E36-MJMAIN-28" x="0" y="0"/><g transform="translate(389,0)"><use xlink:href="#E36-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E36-MJMAIN-31"/><use transform="scale(0.707)" xlink:href="#E36-MJMAIN-31" x="500" y="0"/></g></g><use xlink:href="#E36-MJMAIN-2B" x="2133" y="0"/><g transform="translate(3133,0)"><use xlink:href="#E36-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E36-MJMAIN-31"/><use transform="scale(0.707)" xlink:href="#E36-MJMAIN-32" x="500" y="0"/></g></g><use xlink:href="#E36-MJMAIN-29" x="4655" y="0"/></g><g transform="translate(8034,0)"><use xlink:href="#E36-MJMATHI-3B4" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E36-MJMAIN-32" x="640" y="513"/></g></g></svg></span></p><p>再设定<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="16.049ex" height="2.86ex" viewbox="0 -861.1 6910.1 1231.2" role="img" focusable="false" style="vertical-align: -0.86ex;"><defs><path stroke-width="0" id="E37-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"/><path stroke-width="0" id="E37-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"/><path stroke-width="0" id="E37-MJMATHI-3B4" d="M195 609Q195 656 227 686T302 717Q319 716 351 709T407 697T433 690Q451 682 451 662Q451 644 438 628T403 612Q382 612 348 641T288 671T249 657T235 628Q235 584 334 463Q401 379 401 292Q401 169 340 80T205 -10H198Q127 -10 83 36T36 153Q36 286 151 382Q191 413 252 434Q252 435 245 449T230 481T214 521T201 566T195 609ZM112 130Q112 83 136 55T204 27Q233 27 256 51T291 111T309 178T316 232Q316 267 309 298T295 344T269 400L259 396Q215 381 183 342T137 256T118 179T112 130Z"/><path stroke-width="0" id="E37-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"/><path stroke-width="0" id="E37-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"/><path stroke-width="0" id="E37-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E37-MJMAIN-3D" x="0" y="0"/><use xlink:href="#E37-MJMAIN-28" x="1055" y="0"/><use xlink:href="#E37-MJMATHI-3B4" x="1444" y="0"/><use xlink:href="#E37-MJMAIN-2C" x="1895" y="0"/><use xlink:href="#E37-MJMATHI-3B4" x="2340" y="0"/><use xlink:href="#E37-MJMAIN-2C" x="2791" y="0"/><use xlink:href="#E37-MJMATHI-3B4" x="3236" y="0"/><use xlink:href="#E37-MJMAIN-2C" x="3687" y="0"/><use xlink:href="#E37-MJMAIN-30" x="4131" y="0"/><use xlink:href="#E37-MJMAIN-2C" x="4631" y="0"/><use xlink:href="#E37-MJMAIN-30" x="5076" y="0"/><use xlink:href="#E37-MJMAIN-2C" x="5576" y="0"/><use xlink:href="#E37-MJMAIN-30" x="6021" y="0"/><use xlink:href="#E37-MJMAIN-29" x="6521" y="0"/></g></svg></span> ，可得<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="23.584ex" height="3.857ex" viewbox="0 -1045.1 10154.4 1660.8" role="img" focusable="false" style="vertical-align: -1.43ex;"><defs><path stroke-width="0" id="E38-MJMAIN-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"/><path stroke-width="0" id="E38-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"/><path stroke-width="0" id="E38-MJMATHI-56" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"/><path stroke-width="0" id="E38-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"/><path stroke-width="0" id="E38-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"/><path stroke-width="0" id="E38-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"/><path stroke-width="0" id="E38-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"/><path stroke-width="0" id="E38-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"/><path stroke-width="0" id="E38-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"/><path stroke-width="0" id="E38-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"/><path stroke-width="0" id="E38-MJMAIN-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 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transform="scale(0.707)" xlink:href="#E38-MJMAIN-31"/><use transform="scale(0.707)" xlink:href="#E38-MJMAIN-31" x="500" y="0"/></g></g><use xlink:href="#E38-MJMAIN-2B" x="2133" y="0"/><use xlink:href="#E38-MJMAIN-32" x="3133" y="0"/><g transform="translate(3633,0)"><use xlink:href="#E38-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E38-MJMAIN-31"/><use transform="scale(0.707)" xlink:href="#E38-MJMAIN-32" x="500" y="0"/></g></g><use xlink:href="#E38-MJMAIN-29" x="5155" y="0"/></g><g transform="translate(9247,0)"><use xlink:href="#E38-MJMATHI-3B4" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E38-MJMAIN-32" x="640" y="513"/></g></g></svg></span> 。</p><p>联立以上三个方程组，即可得到三个独立弹性常数。</p><p>施加形变后的晶格基矢可通过下式得到 [2]:</p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n305" cid="n305" mdtype="math_block"><div class="md-rawblock-container md-math-container" 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transform="translate(6227,2536)"><use xlink:href="#E7-MJSZ4-239E" x="0" y="-1154"/><g transform="translate(0,-2795.4620670846252) scale(1,1.6991181427616808)"><use xlink:href="#E7-MJSZ4-239F"/></g><use xlink:href="#E7-MJSZ4-23A0" x="0" y="-3930"/></g></g></g></svg></span></div></div></div><p><code>VASPKIT</code>和VASP计算晶体的弹性常数具体计算步骤分为：</p><ol start=""><li>准备优化彻底的POSCAR文件，注意通常采用标准的惯用原胞计算弹性常数；</li><li>运行<code>vaspkit</code> 选择<code>102</code>生成KPOINTS，由于计算弹性常数对<code>K-mesh</code>要求很高，因此对于半导体（金属体）体系，生成K点的精度应不小于<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.397ex" height="2.86ex" viewbox="0 -861.1 6629.4 1231.2" role="img" focusable="false" style="vertical-align: -0.86ex;"><defs><path stroke-width="0" id="E40-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 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-247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"/><path stroke-width="0" id="E40-MJMAIN-D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"/><path stroke-width="0" id="E40-MJMATHI-3C0" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E40-MJMAIN-30"/><use xlink:href="#E40-MJMAIN-2E" x="500" y="0"/><use xlink:href="#E40-MJMAIN-30" x="778" y="0"/><use xlink:href="#E40-MJMAIN-33" x="1278" y="0"/><use xlink:href="#E40-MJMAIN-28" x="1778" y="0"/><g transform="translate(2167,0)"><use xlink:href="#E40-MJMAIN-30"/><use xlink:href="#E40-MJMAIN-2E" x="500" y="0"/><use xlink:href="#E40-MJMAIN-30" x="778" y="0"/><use xlink:href="#E40-MJMAIN-32" x="1278" y="0"/></g><use xlink:href="#E40-MJMAIN-29" x="3945" y="0"/><use xlink:href="#E40-MJMAIN-D7" x="4556" y="0"/><use xlink:href="#E40-MJMAIN-32" x="5556" y="0"/><use xlink:href="#E40-MJMATHI-3C0" x="6056" y="0"/></g></svg></span>  <span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.914ex" height="3.002ex" viewbox="0 -983.8 1685.4 1292.6" role="img" focusable="false" style="vertical-align: -0.717ex;"><defs><path stroke-width="0" id="E41-MJMAIN-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"/><path stroke-width="0" id="E41-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><text font-family="STIXGeneral,'Arial Unicode MS',serif" stroke="none" transform="scale(61.362) matrix(1 0 0 -1 0 0)">Å</text><g transform="translate(681,408)"><use transform="scale(0.707)" xlink:href="#E41-MJMAIN-2212" x="0" y="0"/><use transform="scale(0.707)" xlink:href="#E41-MJMAIN-31" x="778" y="0"/></g></g></svg></span></li><li>INCAR参考设置如下；</li></ol><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>19</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Global Parameters</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  ISTART =  0        </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  LREAL  =  F      </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  PREC   =  High  （截断能设置默认值1.5-2倍）</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  LWAVE  = F       </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  LCHARG = F     </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  ADDGRID= .TRUE.    </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Electronic Relaxation</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  ISMEAR =  0          </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  SIGMA  =  0.05       </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  NELM   =  40           </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  NELMIN =  4           </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  EDIFF  =  1E-08       </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Ionic Relaxation</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  NELMIN =  6          </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  NSW    =  100         </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  IBRION =  2           </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">18</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  ISIF   =  2    （切记选择2,如果选择3会把施加应变后原胞重新优化成平衡原胞）</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">19</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  EDIFFG = -1E-02  </span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 380px;"/><div class="CodeMirror-gutters" style="height: 380px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><ol start="4"><li>准备<code>VPKIT.in</code>文件并设置第一行为1（预处理）；运行<code>vaspkit</code>并选择<code>201</code>, 生成用于计算弹性常数文件；</li></ol><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>4</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">1                    ! 设置1将产生计算弹性常数的输入文件，2则计算弹性常数</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">3D                   ! 2D为二维体系，3D为三维体系</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">7                    ! 7个应变</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">-0.015 -0.010 -0.005 0.000 0.005 0.010 0.015  ! 应变变化范围</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 80px;"/><div class="CodeMirror-gutters" style="height: 80px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>    5.批量提交vasp作业；</p><ol start="6"><li>再次修改<code>VPKIT.in</code>文件中第一行为2，然后再次运行<code>vaspkit</code>并选择<code>201</code>，得到以下结果；</li></ol><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 48.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 34px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>63</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -34px; width: 34px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  -->> (01) Reading VPKIT.in File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +-------------------------- Warm Tips --------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">      See an example in vaspkit/examples/elastic/diamond_3D,</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   Require the fully-relaxed and standardized Convertional cell.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  -->> (02) Reading Structural Parameters from POSCAR File...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  -->> (03) Calculating the fitting coefficients of energy vs strain.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> -->> Current directory: Fitting Precision</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                    C44:  0.817E-09  （拟合精度应保证低于1E-7，否则检查个别体系是否收敛）</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                C11_C22:  0.814E-08</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">                C11_C12:  0.135E-07</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +-------------------------- Summary ----------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Based on the Strain versus Energy method.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Crystal Class: m-3m</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Space Group: Fd-3m</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Crystal System: Cubic system</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Including Point group classes: 23, 2/m-3, 432, -43m, 4/m-32/m</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">18</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> There are 3 independent elastic constants</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">19</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    C11  C12  C12    0    0    0</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">20</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    C12  C11  C12    0    0    0</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">21</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    C12  C12  C11    0    0    0</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">22</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">      0    0    0  C44    0    0</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">23</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">      0    0    0    0  C44    0</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">24</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">      0    0    0    0    0  C44</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">25</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">26</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Stiffness Tensor C_ij (in GPa):</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">27</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   1050.640    126.640    126.640      0.000      0.000      0.000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">28</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    126.640   1050.640    126.640      0.000      0.000      0.000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">29</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">    126.640    126.640   1050.640      0.000      0.000      0.000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">30</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">      0.000      0.000      0.000    559.861      0.000      0.000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">31</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">      0.000      0.000      0.000      0.000    559.861      0.000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">32</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">      0.000      0.000      0.000      0.000      0.000    559.861</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">33</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">34</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Compliance Tensor S_ij (in GPa^{-1}):</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">35</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.000977  -0.000105  -0.000105   0.000000   0.000000   0.000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">36</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  -0.000105   0.000977  -0.000105   0.000000   0.000000   0.000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">37</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">  -0.000105  -0.000105   0.000977   0.000000   0.000000   0.000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">38</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.000000   0.000000   0.000000   0.001786   0.000000   0.000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">39</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.000000   0.000000   0.000000   0.000000   0.001786   0.000000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">40</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">   0.000000   0.000000   0.000000   0.000000   0.000000   0.001786</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">41</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">42</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Average mechanical properties for polycrystalline:</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">43</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">44</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> | Scheme |   Bulk K   |  Young's E  |   Shear G  |  Poisson's v |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">45</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">46</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |  Voigt | 434.64 GPa | 1116.34 GPa | 520.72 GPa |     0.07     |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">47</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |  Reuss | 434.64 GPa | 1109.30 GPa | 516.13 GPa |     0.07     |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">48</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> |  Hill  | 434.64 GPa | 1112.82 GPa | 518.42 GPa |     0.07     |</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">49</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">50</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Pugh Ratio:     1.19</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">51</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Cauchy Pressure (GPa):  -433.22</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">52</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Universal Elastic Anisotropy: 0.04</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">53</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Chung–Buessem Anisotropy:     0.00</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">54</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Isotropic Poisson’s Ratio:    0.07</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">55</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">56</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Voigt averaging scheme gives the upper bound for polycrystalline.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">57</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Reuss averaging scheme gives the lower bound for polycrystalline.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">58</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> Hill averaging scheme is the average of Reuss's and Voigt's data.</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">59</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> References:</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">60</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> [1] Voigt W, Lehrbuch der Kristallphysik (1928)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">61</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> [2] Reuss A, Z. Angew. Math. Mech. 9 49–58 (1929)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 26px;">62</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> [3] Hill R, Proc. Phys. Soc. A 65 349–54 (1952)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -34px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 26px;">63</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> +---------------------------------------------------------------+</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 1260px;"/><div class="CodeMirror-gutters" style="height: 1260px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 34px;"/></div></div></div></pre><p>金刚石弹性常数实验值分别为：<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="11.278ex" height="2.432ex" viewbox="0 -799.7 4855.7 1047.1" role="img" focusable="false" style="vertical-align: -0.575ex;"><defs><path stroke-width="0" id="E42-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"/><path stroke-width="0" id="E42-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"/><path stroke-width="0" id="E42-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"/><path stroke-width="0" id="E42-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"/><path stroke-width="0" id="E42-MJMAIN-37" d="M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z"/><path stroke-width="0" id="E42-MJMAIN-39" d="M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E42-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E42-MJMAIN-31"/><use transform="scale(0.707)" xlink:href="#E42-MJMAIN-31" x="500" y="0"/></g><use xlink:href="#E42-MJMAIN-3D" x="1799" y="0"/><g transform="translate(2855,0)"><use xlink:href="#E42-MJMAIN-31"/><use xlink:href="#E42-MJMAIN-30" x="500" y="0"/><use xlink:href="#E42-MJMAIN-37" x="1000" y="0"/><use xlink:href="#E42-MJMAIN-39" x="1500" y="0"/></g></g></svg></span>  GPa, <span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.116ex" height="2.432ex" viewbox="0 -799.7 4355.7 1047.1" role="img" focusable="false" style="vertical-align: -0.575ex;"><defs><path stroke-width="0" id="E43-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"/><path stroke-width="0" id="E43-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"/><path stroke-width="0" id="E43-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"/><path stroke-width="0" id="E43-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"/><path stroke-width="0" id="E43-MJMAIN-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E43-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E43-MJMAIN-31"/><use transform="scale(0.707)" xlink:href="#E43-MJMAIN-32" x="500" y="0"/></g><use xlink:href="#E43-MJMAIN-3D" x="1799" y="0"/><g transform="translate(2855,0)"><use xlink:href="#E43-MJMAIN-31"/><use xlink:href="#E43-MJMAIN-32" x="500" y="0"/><use xlink:href="#E43-MJMAIN-34" x="1000" y="0"/></g></g></svg></span>  GPa和<span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.116ex" height="2.432ex" viewbox="0 -799.7 4355.7 1047.1" role="img" focusable="false" style="vertical-align: -0.575ex;"><defs><path stroke-width="0" id="E44-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"/><path stroke-width="0" id="E44-MJMAIN-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"/><path stroke-width="0" id="E44-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"/><path stroke-width="0" id="E44-MJMAIN-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"/><path stroke-width="0" id="E44-MJMAIN-37" d="M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z"/><path stroke-width="0" id="E44-MJMAIN-38" d="M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z"/></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E44-MJMATHI-43" x="0" y="0"/><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#E44-MJMAIN-34"/><use transform="scale(0.707)" xlink:href="#E44-MJMAIN-34" x="500" y="0"/></g><use xlink:href="#E44-MJMAIN-3D" x="1799" y="0"/><g transform="translate(2855,0)"><use xlink:href="#E44-MJMAIN-35"/><use xlink:href="#E44-MJMAIN-37" x="500" y="0"/><use xlink:href="#E44-MJMAIN-38" x="1000" y="0"/></g></g></svg></span>  GPa [3],通过比较发现采用VASPKIT结合VASP得到的理论计算弹性常数与实验值符合较好。</p><p><strong>参考文献：</strong></p><p>[1] 武松，利用 VASP 计算不同晶系晶体弹性常数</p><p>[2] 侯柱锋，采用VASP如何计算晶体的弹性常数</p><p>[3] McSkimin H J and Andreatch P 1972 J. Appl. Phys. 43 2944</p><p> </p><h4><a name="header-n332" class="md-header-anchor "/>3.12 用VASPKIT计算有效质量</h4><p>以 <code>MoS2</code> 单层为例，首先通过分析能带结构找出<strong>价带顶(VBM)</strong>和<strong>导带底(CBM)</strong>的位置。对于 MoS2 单层，其价带顶和导带底均位于高对称点K点处。</p><div align="center"><img src="MoS2单层能带结构.png" width="60%" height="60%" onerror="this.style.display = 'none';"/></div><p>接下来我们计算K点处沿着 <code>K -> Γ</code> 和 <code>K -> M</code>方向的电子及空穴载流子的有效质量；</p><ul><li>第一步：准备 POSCAR 文件以及 <code>VPKIT.in</code>文件， <code>VPKIT.in</code>文件包含以下内容；</li></ul><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>6</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">1</span> 设置为1将会生成计算有效质量的KPOINTS文件，2则计算有效质量</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">6</span> <span class="cm-number">6</span>表示我们在K附近取6个离散点用于多项式拟合</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">0</span>.015 k-cutoff, 截断半径，典型值0.015 Å-1</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">2</span> <span class="cm-number">2</span> 表示有两个有效质量任务</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">0</span>.333333 <span class="cm-number">0</span>.3333333 <span class="cm-number">0</span>.000 <span class="cm-number">0</span>.000 <span class="cm-number">0</span>.000 <span class="cm-number">0</span>.000 K->Γ 计算K点处有效质量，沿着K指向Γ方向</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">0</span>.333333 <span class="cm-number">0</span>.3333333 <span class="cm-number">0</span>.000 <span class="cm-number">0</span>.500 <span class="cm-number">0</span>.000 <span class="cm-number">0</span>.000 K->M 计算K点处有效质量，沿着K指向M方向</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 120px;"/><div class="CodeMirror-gutters" style="height: 120px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><div align="center"><img src="采用多项式拟合计算载流子有效质量示意图.png" width="60%" height="60%" onerror="this.style.display = 'none';"/></div><ul><li><p>第二步：运行 <code>vaspkit</code>并选择 <code>912</code>或者<code>913</code>产生 KPOINTS ， POTCAR 文件及静态计算 INCAR 文件；</p></li><li><p>第三步：提交 <code>VASP</code>作业；-</p></li><li><p>第四步：计算完成后把 <code>VPKIT.in</code> 文件中第一行的 1 修改为 2 ，然后再次运行 <code>vaspkit</code>并选择 <code>913</code> ，得到以下结果：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>4</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-number">9</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Effective-Mass (in m0) Electron (Prec.) Hole (Prec.)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">K-PATH No.1: K->G <span class="cm-number">0</span>.473 (0.3E-07) <span class="cm-attribute">-0</span>.569 (0.1E-07)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">K-PATH No.2: K->M <span class="cm-number">0</span>.524 (0.1E-06) <span class="cm-attribute">-0</span>.691 (0.1E-06)</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 80px;"/><div class="CodeMirror-gutters" style="height: 80px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p><code>Kormányos</code>等人计算得到 <code>MoS2</code>单层的电子和空穴载流子<strong>有效质量</strong>分别为 0.44 和 0.54 [见文献<strong>2D Mater. 2 (2015) 049501</strong>]
<strong>注意：如果价带顶和导带底存在简并，例如GaAs和GaN等材料，这时候很难保证精度。</strong></p></li></ul><h4><a name="header-n350" class="md-header-anchor "/>3.13 绘制原子电荷着色的结构图 </h4><p><strong>绘制原子电荷着色的结构图</strong>的功能由<code>刘锦程</code>使用<code>python</code>编写，经过优化后整合到了<code>vaspkit0.73</code>版本中、
在算原子电荷的时候(比如：<code>Bader电荷</code>)需要分析总的电荷密度<code>CHGCAR_sum</code>了。所谓的<strong>原子电荷</strong>就是把一定空间内的电荷密度都划分给附近的一个原子，用一套人为的规则定义每个原子上所带的电荷。原子电荷常常用于<strong>定性分析</strong>，非常有用，第一性原理计算最常用的就是Bader电荷了。</p><p>计算<code>bader电荷</code>需要在<code>INCAR</code>里添加关键词<code>LAECHG=.TRUE.</code>：</p><p>开始会产生<code>AECCAR0 AECCAR1</code>两个文件，分别包含内核和内层电子密度(赝势)，初始价层电子密度。计算结束会再生成一个AECCAR2文件，包含SCF收敛以后的价层电子密度。要得到体系的总电荷密度需要将<code>AECCAR0 AECCAR1</code>两个文件的密度叠加，方法就是用一个<code>vtst</code>脚本：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">chgsum.pl AECCAR0 AECCAR2</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p>生成<code>CHGCAR_sum</code>，然后计算<code>bader电荷</code>：</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="bash"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="bash"><div style="overflow: hidden; position: relative; width: 3px; ; top: 6.5px; left: 40.5px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"/></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"/><div class="CodeMirror-gutter-filler" cm-not-content="true"/><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>1</div></div></div><div class="CodeMirror-measure"/><div style="position: relative; z-index: 1;"/><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"/><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"/><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">bader CHGCAR –ref CHGCAR_sum</span></pre></div></div></div></div></div></div><div style="position: absolute; ; width: 1px; border-bottom: 0px solid transparent; top: 20px;"/><div class="CodeMirror-gutters" style="height: 20px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"/></div></div></div></pre><p><code>bader</code>是一个二进制可执行文件，在<a href="http://theory.cm.utexas.edu/henkelman/code/bader/">此网站</a>可以下载最新版的<code>bader</code>程序。</p><p>运行成功会生成三个文件：<code>ACF.dat, BCF.dat, AVF.dat</code></p> <div align="center"><img src="acf.jpg" width="70%" height="70%" onerror="this.style.display = 'none';"/></div><p>其中<code>ACF.dat</code>文件包含：原子坐标和每个原子的价层电子数目，通过对比价电子数和<code>POTCAR</code>中的<code>ZVAL</code>就能得到每个原子的<code>bader</code>电荷。由此可以进一步计算体系的<code>bader</code>电荷着色的的结构图。</p><p>启动<code>vaspkit</code>，选择功能<code>508</code>，<code>Bader2PQR (Shown in VMD by atomic charge)</code>，<code>vaspkit</code>会执行<code>utilities</code>下的<code>bader2pqr.py</code>，运行结束后，将会得到<code>bader.pqr</code>和<code>vmdrc.txt</code>文件，用<code>VMD</code>可以打开<code>bader.pqr</code>文件也可以将其直接拖入主显示窗口。
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